Asymptotic Vassiliev invariants for vector fields

Sebastian Baader; Julien Marché

Displaying similar documents to “Asymptotic Vassiliev invariants for vector fields”

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...

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...

Degree three cohomological invariants of semisimple groups

Alexander Merkurjev (2016)

Journal of the European Mathematical Society

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We study the degree 3 cohomological invariants with coefficients in $ℚ / ℤ (2)$ of a semisimple group over an arbitrary field. A list of all invariants of adjoint groups of inner type is given.

Brunnian local moves of knots and Vassiliev invariants

Akira Yasuhara (2006)

Fundamenta Mathematicae

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K. Habiro gave a neccesary and sufficient condition for knots to have the same Vassiliev invariants in terms of $C_{k}$ -moves. In this paper we give another geometric condition in terms of Brunnian local moves. The proof is simple and self-contained.

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.

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

R. J. Lawrence (1995)

Recherche Coopérative sur Programme n°25

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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.

Analytic invariants for the $1 : - 1$ resonance

José Pedro Gaivão (2013)

Annales de l’institut Fourier

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Associated to analytic Hamiltonian vector fields in $ℂ^{4}$ having an equilibrium point satisfying a non semisimple $1 : - 1$ resonance, we construct two constants that are invariant with respect to local analytic symplectic changes of coordinates. These invariants vanish when the Hamiltonian is integrable. We also prove that one of these invariants does not vanish on an open and dense set.

Smooth invariants and $ω$ -graded modules over $k [X]$

Fred Richman (2000)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that every $ω$ -graded module over $k [X]$ is a direct sum of cyclics. The invariants for such modules are exactly the smooth invariants of valuated abelian $p$ -groups.

$Q$ -curvature and spectral invariants

Branson, Thomas

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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).

On isomorphic classification of tensor products $E_{\infty} (a) \otimes ̂ E_{\infty}^{'} (b)$

Goncharov A., Zahariuta V., Terzioğlu Tosun

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Abstract New linear topological invariants are introduced and utilized to give an isomorphic classification of tensor products of the type $E_{\infty} (a) \otimes ̂ E_{\infty}^{'} (b)$ , where $E_{\infty} (a)$ is a power series space of infinite type. These invariants are modifications of those suggested earlier by Zahariuta. In particular, some new results are obtained for spaces of infinitely differentiable functions with values in a locally convex space X. These spaces coincide, up to isomorphism, with spaces L(s’,X) of all continuous linear...

On the colored Jones polynomials of ribbon links, boundary links and Brunnian links

Sakie Suzuki (2014)

Banach Center Publications

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Habiro gave principal ideals of $ℤ [q, q^{- 1}]$ in which certain linear combinations of the colored Jones polynomials of algebraically-split links take values. The author proved that the same linear combinations for ribbon links, boundary links and Brunnian links are contained in smaller ideals of $ℤ [q, q^{- 1}]$ generated by several elements. In this paper, we prove that these ideals also are principal, each generated by a product of cyclotomic polynomials.

Labeled floor diagrams for plane curves

Sergey Fomin, Grigory Mikhalkin (2010)

Journal of the European Mathematical Society

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Floor diagrams are a class of weighted oriented graphs introduced by E. Brugallé and the second author. Tropical geometry arguments lead to combinatorial descriptions of (ordinary and relative) Gromov–Witten invariants of projective spaces in terms of floor diagrams and their generalizations. In a number of cases, these descriptions can be used to obtain explicit (direct or recursive) formulas for the corresponding enumerative invariants. In particular, we use this approach to enumerate...

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....

Governing fields for the 2-classgroup of $Q (s q r t - q_{1} q_{2} p)$ and a related reciprocity law

Patrick Morton (1990)

Acta Arithmetica

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On the bounding, splitting, and distributivity numbers

Alan S. Dow, Saharon Shelah (2023)

Commentationes Mathematicae Universitatis Carolinae

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The cardinal invariants $𝔥, 𝔟, 𝔰$ of $𝒫 (ω)$ are known to satisfy that $ω_{1} \leq 𝔥 \leq min {𝔟, 𝔰}$ . We prove that all inequalities can be strict. We also introduce a new upper bound for $𝔥$ and show that it can be less than $𝔰$ . The key method is to utilize finite support matrix iterations of ccc posets following paper Ultrafilters with small generating sets by A. Blass and S. Shelah (1989).

$H^{p}$ -spaces of conjugate systems on local fields

Jia Chao (1974)

Studia Mathematica

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Subfields of henselian valued fields

Ramneek Khassa, Sudesh K. Khanduja (2010)

Colloquium Mathematicae

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Let (K,v) be a henselian valued field of arbitrary rank which is not separably closed. Let k be a subfield of K of finite codimension and $v_{k}$ be the valuation obtained by restricting v to k. We give some necessary and sufficient conditions for $(k, v_{k})$ to be henselian. In particular, it is shown that if k is dense in its henselization, then $(k, v_{k})$ is henselian. We deduce some well known results proved in this direction through other considerations.