Asymptotic Expansions of Witten-Reshetikhin-Turaev Invariants for Some Simple $3$-Manifolds

R. J. Lawrence

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Witten's Conjecture for many four-manifolds of simple type

Paul M. N. Feehan, Thomas G. Leness (2015)

Journal of the European Mathematical Society

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We prove that Witten’s Conjecture [40] on the relationship between the Donaldson and Seiberg-Witten series for a four-manifold of Seiberg-Witten simple type with $b_{1} = 0$ and odd $b_{2}^{+} \geq 3$ follows from our $(3)$ -monopole cobordism formula [6] when the four-manifold has $c_{1}^{2} \geq χ_{h} - 3$ or is abundant.

The Seiberg–Witten invariants of negative definite plumbed 3-manifolds

András Némethi (2011)

Journal of the European Mathematical Society

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Assume that $Γ$ is a connected negative definite plumbing graph, and that the associated plumbed 3-manifold $M$ is a rational homology sphere. We provide two new combinatorial formulae for the Seiberg–Witten invariant of $M$ . The first one is the constant term of a ‘multivariable Hilbert polynomial’, it reflects in a conceptual way the structure of the graph $Γ$ , and emphasizes the subtle parallelism between these topological invariants and the analytic invariants of normal surface singularities....

Cocycle invariants of codimension 2 embeddings of manifolds

Józef H. Przytycki, Witold Rosicki (2014)

Banach Center Publications

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We consider the classical problem of a position of n-dimensional manifold Mⁿ in $ℝ^{n + 2}$ . We show that we can define the fundamental (n+1)-cycle and the shadow fundamental (n+2)-cycle for a fundamental quandle of a knotting $M ⁿ \to ℝ^{n + 2}$ . In particular, we show that for any fixed quandle, quandle coloring, and shadow quandle coloring, of a diagram of Mⁿ embedded in $ℝ^{n + 2}$ we have (n+1)- and (n+2)-(co)cycle invariants (i.e. invariant under Roseman moves).

Two cases when $d_{κ}$ and $d *_{κ}$ are equal

Ofer Shafir (2001)

Fundamenta Mathematicae

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We deal with two cardinal invariants and give conditions on their equality using Shelah's pcf theory.

Welschinger invariants of small non-toric Del Pezzo surfaces

Ilia Itenberg, Viatcheslav Kharlamov, Eugenii Shustin (2013)

Journal of the European Mathematical Society

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We give a recursive formula for purely real Welschinger invariants of the following real Del Pezzo surfaces: the projective plane blown up at $\sim q$ real and $s \leq 1$ pairs of conjugate imaginary points, where $q + 2 s \leq 5$ , and the real quadric blown up at $s \leq 1$ pairs of conjugate imaginary points and having non-empty real part. The formula is similar to Vakil’s recursive formula [22] for Gromov–Witten invariants of these surfaces and generalizes our recursive formula [12] for purely real Welschinger invariants...

Pseudosymmetric and Weyl-pseudosymmetric $(κ, μ)$ -contact metric manifolds

N. Malekzadeh, E. Abedi, U.C. De (2016)

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In this paper we classify pseudosymmetric and Ricci-pseudosymmetric $(κ, μ)$ -contact metric manifolds in the sense of Deszcz. Next we characterize Weyl-pseudosymmetric $(κ, μ)$ -contact metric manifolds.

How to define "convex functions" on differentiable manifolds

Stefan Rolewicz (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: $1_{}$ . if M is a linear manifold, then (M) contains convex functions, $2_{}$ . (·) is invariant under diffeomorphisms, $3_{}$ . each f ∈ (M) is differentiable on a dense $G_{δ}$ -set, is investigated.

The obstruction to the deformation of a map out of a subspace

R. Dobreńko

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Introduction1. Preliminaries.............................................................................................52. The obstruction to the deformation of a map out of a subspace.............123. The case of smooth closed oriented manifolds.......................................174. The invariant $o_{B} (f)$ for PD-spaces.....................................................215. The local case of obstruction theory.......................................................24References.................................................................................................29 ...

Generalised Weber functions

Andreas Enge, François Morain (2014)

Acta Arithmetica

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A generalised Weber function is given by $_{N} (z) = η (z / N) / η (z)$ , where η(z) is the Dedekind function and N is any integer; the original function corresponds to N=2. We classify the cases where some power $_{N}^{e}$ evaluated at some quadratic integer generates the ring class field associated to an order of an imaginary quadratic field. We compare the heights of our invariants by giving a general formula for the degree of the modular equation relating $_{N} (z)$ and j(z). Our ultimate goal is the use of these invariants in...

A Proof Via the Seiberg-Witten Moduli Space of Donaldson’s Theorem on Smooth $4$ -Manifolds with Definite Intersection Forms

Mikhail Katz (1995)

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Exotic Deformations of Calabi-Yau Manifolds

Paolo de Bartolomeis, Adriano Tomassini (2013)

Annales de l’institut Fourier

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We introduce Quantum Inner State manifolds (QIS manifolds) as (compact) $2 n$ -dimensional symplectic manifolds $(M, κ)$ endowed with a $κ$ -tamed almost complex structure $J$ and with a nowhere vanishing and normalized section $ϵ$ of the bundle $Λ_{J}^{n, 0} (M)$ satisfying the condition ${\bar{\partial}}_{J} ϵ = 0$ . We study the moduli space $𝔐$ of QIS deformations of a given Calabi-Yau manifold, computing its tangent space...

Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers

Robert Lipshitz, David Treumann (2016)

Journal of the European Mathematical Society

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Let $A$ be a dg algebra over $𝔽_{2}$ and let $M$ be a dg $A$ -bimodule. We show that under certain technical hypotheses on $A$ , a noncommutative analog of the Hodge-to-de Rham spectral sequence starts at the Hochschild homology of the derived tensor product $M \otimes_{A}^{L} M$ and converges to the Hochschild homology of $M$ . We apply this result to bordered Heegaard Floer theory, giving spectral sequences associated to Heegaard Floer homology groups of certain branched and unbranched double covers.

Injective comodules and Landweber exact homology theories

Mark Hovey (2007)

Fundamenta Mathematicae

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We classify the indecomposable injective E(n)⁎E(n)-comodules, where E(n) is the Johnson-Wilson homology theory. They are suspensions of the $J_{n, r} = E (n) ⁎ (M_{r} E (r))$ , where 0 ≤ r ≤ n, with the endomorphism ring of $J_{n, r}$ being $\hat{E (r)} * \hat{E (r)}$ , where $\hat{E (r)}$ denotes the completion of E(r).

Riemannian regular $σ$ -manifolds

A. A. Ermolitski (1994)

Czechoslovak Mathematical Journal

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Homotopy invariance of higher signatures and $3$ -manifold groups

Michel Matthey, Hervé Oyono-Oyono, Wolfgang Pitsch (2008)

Bulletin de la Société Mathématique de France

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For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable $3$ -manifolds, including the “piecewise geometric” ones in the sense of Thurston. In particular, this class, that will be carefully described, is the class of all orientable $3$ -manifolds if the Thurston Geometrization Conjecture is true. In fact, for this type of groups, we show that the Baum-Connes Conjecture With Coefficients...

Topology of Fatou components for endomorphisms of $ℂ ℙ^{k}$ : linking with the Green’s current

Suzanne Lynch Hruska, Roland K. W. Roeder (2010)

Fundamenta Mathematicae

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Little is known about the global topology of the Fatou set U(f) for holomorphic endomorphisms $f : ℂ ℙ^{k} \to ℂ ℙ^{k}$ , when k >1. Classical theory describes U(f) as the complement in $ℂ ℙ^{k}$ of the support of a dynamically defined closed positive (1,1) current. Given any closed positive (1,1) current S on $ℂ ℙ^{k}$ , we give a definition of linking number between closed loops in $ℂ ℙ^{k} ∖ s u p p S$ and the current S. It has the property that if lk(γ,S) ≠ 0, then γ represents a non-trivial homology element in $H ₁ (ℂ ℙ^{k} ∖ s u p p S)$ . As an application, we use...

On the principle of real moduli flexibility: perfect parametrizations

Edoardo Ballico, Riccardo Ghiloni (2014)

Annales Polonici Mathematici

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Let V be a real algebraic manifold of positive dimension. The aim of this paper is to show that, for every integer b (arbitrarily large), there exists a trivial Nash family $= {V_{y}}_{y \in R^{b}}$ of real algebraic manifolds such that V₀ = V, is an algebraic family of real algebraic manifolds over $y \in R^{b} ∖ 0$ (possibly singular over y = 0) and is perfectly parametrized by $R^{b}$ in the sense that $V_{y}$ is birationally nonisomorphic to $V_{z}$ for every $y, z \in R^{b}$ with y ≠ z. A similar result continues to hold if V is a singular real algebraic...

The ℤ₂-cohomology cup-length of real flag manifolds

Július Korbaš, Juraj Lörinc (2003)

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Using fiberings, we determine the cup-length and the Lyusternik-Shnirel’man category for some infinite families of real flag manifolds $O (n ₁ + . . . + n_{q}) / O (n ₁) \times . . . \times O (n_{q})$ , q ≥ 3. We also give, or describe ways to obtain, interesting estimates for the cup-length of any $O (n ₁ + . . . + n_{q}) / O (n ₁) \times . . . \times O (n_{q})$ , q ≥ 3. To present another approach (combining well with the “method of fiberings”), we generalize to the real flag manifolds Stong’s approach used for calculations in the ℤ₂-cohomology algebra of the Grassmann manifolds.

Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps

Martine Babillot, Marc Peigné (2006)

Bulletin de la Société Mathématique de France

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We consider a large class of non compact hyperbolic manifolds $M = ℍ^{n} / Γ$ with cusps and we prove that the winding process $(Y_{t})$ generated by a closed $1$ -form supported on a neighborhood of a cusp $𝒞$ , satisfies a limit theorem, with an asymptotic stable law and a renormalising factor depending only on the rank of the cusp $𝒞$ and the Poincaré exponent $δ$ of $Γ$ . No assumption on the value of $δ$ is required and this theorem generalises previous results due to Y. Guivarc’h, Y. Le Jan, J. Franchi and N. Enriquez. ...

Global integral formulas for solving the $\bar{\partial}$ -equation on Stein manifolds

Gennadi M. Henkin, Jürgen Leiterer (1981)

Annales Polonici Mathematici

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Admissibly integral manifolds for semilinear evolution equations

Nguyen Thieu Huy, Vu Thi Ngoc Ha (2014)

Annales Polonici Mathematici

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We prove the existence of integral (stable, unstable, center) manifolds of admissible classes for the solutions to the semilinear integral equation $u (t) = U (t, s) u (s) + \int_{s}^{t} U (t, ξ) f (ξ, u (ξ)) d ξ$ when the evolution family ${(U (t, s))}_{t \geq s}$ has an exponential trichotomy on a half-line or on the whole line, and the nonlinear forcing term f satisfies the (local or global) φ-Lipschitz conditions, i.e., ||f(t,x)-f(t,y)|| ≤ φ(t)||x-y|| where φ(t) belongs to some classes of admissible function spaces. These manifolds are formed by trajectories of the...

Holonomy groups of flat manifolds with the $R_{\infty}$ property

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Fundamenta Mathematicae

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Let M be a flat manifold. We say that M has the $R_{\infty}$ property if the Reidemeister number R(f) is infinite for every homeomorphism f: M → M. We investigate relations between the holonomy representation ρ of M and the $R_{\infty}$ property. When the holonomy group of M is solvable we show that if ρ has a unique ℝ-irreducible subrepresentation of odd degree then M has the $R_{\infty}$ property. This result is related to Conjecture 4.8 in [K. Dekimpe et al., Topol. Methods Nonlinear Anal. 34 (2009)].

On the $L^{p}$ index of spin Dirac operators on conical manifolds

André Legrand, Sergiu Moroianu (2006)

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We compute the index of the Dirac operator on a spin Riemannian manifold with conical singularities, acting from $L^{p} (Σ ⁺)$ to $L^{q} (Σ ¯)$ with p,q > 1. When 1 + n/p - n/q > 0 we obtain the usual Atiyah-Patodi-Singer formula, but with a spectral cut at (n+1)/2 - n/q instead of 0 in the definition of the eta invariant. In particular we reprove Chou’s formula for the L² index. For 1 + n/p - n/q ≤ 0 the index formula contains an extra term related to the Calderón projector.

Homological computations in the universal Steenrod algebra

A. Ciampella, L. A. Lomonaco (2004)

Fundamenta Mathematicae

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We study the (bigraded) homology of the universal Steenrod algebra Q over the prime field ₂, and we compute the groups $H_{s, s} (Q)$ , s ≥ 0, using some ideas and techniques of Koszul algebras developed by S. Priddy in [5], although we presently do not know whether or not Q is a Koszul algebra. We also provide an explicit formula for the coalgebra structure of the diagonal homology $D ⁎ (Q) = ⨁_{s \geq 0} H_{s, s} (Q)$ and show that D⁎(Q) is isomorphic to the coalgebra of invariants Γ introduced by W. Singer in [6].

Displaying similar documents to “Asymptotic Expansions of Witten-Reshetikhin-Turaev Invariants for Some Simple 3 -Manifolds”

Displaying similar documents to “Asymptotic Expansions of Witten-Reshetikhin-Turaev Invariants for Some Simple $3$ -Manifolds”