Cobordisms of fold maps of 2k+2-manifolds into $ℝ^{3k+2}$

Tamás Terpai

Displaying similar documents to “Cobordisms of fold maps of 2k+2-manifolds into $ℝ^{3 k + 2}$ ”

Non-embeddable $1$ -convex manifolds

Jan Stevens (2014)

Annales de l’institut Fourier

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We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable $1$ -convex manifold. We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type $(1, - 3)$ . To this end we study small resolutions of $c D_{4}$ -singularities.

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

André Legrand, Sergiu Moroianu (2006)

Studia Mathematica

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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.

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...

On the classification of real mono-germs of corank one and codimension one

Kevin Houston (2004)

Banach Center Publications

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Corank one mono-germs $f : (ℝ ⁿ, 0) \to (ℝ^{p}, 0)$ , n < p, of $_{e}$ -codimension one are classified by giving an explicit normal form.

Grassmann manifold $V_{3}^{4}$ in the projective space $P_{7}$ with characteristics consisting of a quadric and two planes

Josef Vala (1993)

Mathematica Bohemica

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Some results in the geometry of four-parametric manifolds of three-dimensional spaces in the projective space $P_{7}$ are found. The properties of such a manifold $V_{3}^{4}$ with characteristics consisting of a quadric and two planes are studied. The properties of the manifold dual to $V_{3}^{4}$ are found. Some results in the geometry of linear spaces from [1],[2],[3],[4] are used. The notation of the quantities is the same as in [4].

The Killing Tensors on an $n$ -dimensional Manifold with $S L (n,)$ -structure

Sergey E. Stepanov, Irina I. Tsyganok, Marina B. Khripunova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an $n$ -dimensional differentiable manifold $M$ endowed with an equiaffine $S L (n,)$ -structure and discuss possible applications of obtained results in Riemannian geometry.

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...

On $^{γ (\cdot, \cdot)}$ -subdifferentiable and [+γ]-subdifferentiable Functions

S. Rolewicz (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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Extending Maps in Hilbert Manifolds

Piotr Niemiec (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

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Certain results on extending maps taking values in Hilbert manifolds by maps which are close to being embeddings are presented. Sufficient conditions on a map under which it is extendable by an embedding are given. In particular, it is shown that if X is a completely metrizable space of topological weight not greater than α ≥ ℵ₀, A is a closed set in X and f: X → M is a map into a manifold M modelled on a Hilbert space of dimension α such that $f (X ∖ A) \cap \bar{f (\partial A)} = \emptyset$ , then for every open cover of M there...

Remarks on the behaviour of higher-order derivations on the gluing of differential spaces

Krzysztof Drachal (2015)

Czechoslovak Mathematical Journal

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This paper is about some geometric properties of the gluing of order $k$ in the category of Sikorski differential spaces, where $k$ is assumed to be an arbitrary natural number. Differential spaces are one of possible generalizations of the concept of an infinitely differentiable manifold. It is known that in many (very important) mathematical models, the manifold structure breaks down. Therefore it is important to introduce a more general concept. In this paper, in particular, the behaviour...

$α$ -continuous multivalued maps

J. Eweret (1989)

Matematički Vesnik

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Singularities of Maxwell’s system in non-hilbertian Sobolev spaces

Wided Chikouche, Serge Nicaise (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study the regularity of the solution of the regularized electric Maxwell problem in a polygonal domain with data in $L^{p} {(Ω)}^{2}$ . Using a duality method, we prove a decomposition of the solution into a regular part in the non-Hilbertian Sobolev space $W^{2, p} {(Ω)}^{2}$ and an explicit singular one.

$Z ₂^{k}$ -actions with a special fixed point set

Pedro L. Q. Pergher, Rogério de Oliveira (2005)

Fundamenta Mathematicae

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Let Fⁿ be a connected, smooth and closed n-dimensional manifold satisfying the following property: if $N^{m}$ is any smooth and closed m-dimensional manifold with m > n and $T : N^{m} \to N^{m}$ is a smooth involution whose fixed point set is Fⁿ, then m = 2n. We describe the equivariant cobordism classification of smooth actions $(M^{m}; Φ)$ of the group $G = Z ₂^{k}$ on closed smooth m-dimensional manifolds $M^{m}$ for which the fixed point set of the action is a submanifold Fⁿ with the above property. This generalizes a result of F....

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.

On isomorphisms between fibrations over $T^{k}$ associated with a $T^{k}$ action

Michał Sadowski (1991)

Annales Polonici Mathematici

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Calculation of the avoiding ideal for $Σ^{1, 1}$

Tamás Terpai (2009)

Banach Center Publications

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We calculate the mapping $H * (B O; ℤ ₂) \to H * (K^{1, 0}; ℤ ₂)$ and obtain a generating system of its kernel. As a corollary, bounds on the codimension of fold maps from real projective spaces to Euclidean space are calculated and the rank of a singular bordism group is determined.

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

Rafał Lutowski, Andrzej Szczepański (2013)

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 $G$ -sets and isospectrality

Ori Parzanchevski (2013)

Annales de l’institut Fourier

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We study finite $G$ -sets and their tensor product with Riemannian manifolds, and obtain results on isospectral quotients and covers. In particular, we show the following: If $M$ is a compact connected Riemannian manifold (or orbifold) whose fundamental group has a finite non-cyclic quotient, then $M$ has isospectral non-isometric covers.

Springer fiber components in the two columns case for types $A$ and $D$ are normal

Nicolas Perrin, Evgeny Smirnov (2012)

Bulletin de la Société Mathématique de France

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We study the singularities of the irreducible components of the Springer fiber over a nilpotent element $N$ with $N^{2} = 0$ in a Lie algebra of type $A$ or $D$ (the so-called two columns case). We use Frobenius splitting techniques to prove that these irreducible components are normal, Cohen–Macaulay, and have rational singularities.

$η$ -Ricci Solitons on $η$ -Einstein ${(L C S)}_{n}$ -Manifolds

Shyamal Kumar Hui, Debabrata Chakraborty (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The object of the present paper is to study $η$ -Ricci solitons on $η$ -Einstein ${(L C S)}_{n}$ -manifolds. It is shown that if $ξ$ is a recurrent torse forming $η$ -Ricci soliton on an $η$ -Einstein ${(L C S)}_{n}$ -manifold then $ξ$ is (i) concurrent and (ii) Killing vector field.

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 ...

Commuting involutions whose fixed point set consists of two special components

Pedro L. Q. Pergher, Rogério de Oliveira (2008)

Fundamenta Mathematicae

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Let Fⁿ be a connected, smooth and closed n-dimensional manifold. We call Fⁿ a manifold with property when it has the following property: if $N^{m}$ is any smooth closed m-dimensional manifold with m > n and $T : N^{m} \to N^{m}$ is a smooth involution whose fixed point set is Fⁿ, then m = 2n. Examples of manifolds with this property are: the real, complex and quaternionic even-dimensional projective spaces $R P^{2 n}$ , $C P^{2 n}$ and $H P^{2 n}$ , and the connected sum of $R P^{2 n}$ and any number of copies of Sⁿ × Sⁿ, where Sⁿ is the n-sphere...

The natural operators $T_{| ℳ f ₙ} ⇝ T * T^{r }$ and $T_{| ℳ f ₙ} ⇝ Λ ² T T^{r *}$

W. M. Mikulski (2002)

Colloquium Mathematicae

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Let r and n be natural numbers. For n ≥ 2 all natural operators $T_{| ℳ f ₙ} ⇝ T * T^{r *}$ transforming vector fields on n-manifolds M to 1-forms on $T^{r *} M = J^{r} (M, ℝ) ₀$ are classified. For n ≥ 3 all natural operators $T_{| ℳ f ₙ} ⇝ Λ ² T * T^{r *}$ transforming vector fields on n-manifolds M to 2-forms on $T^{r *} M$ are completely described.

Some remarks providing discontinuous maps on some $C_{p} (X)$ spaces

S. Moll (2008)

Banach Center Publications

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Let X be a completely regular Hausdorff topological space and $C_{p} (X)$ the space of continuous real-valued maps on X endowed with the pointwise topology. A simple and natural argument is presented to show how to construct on the space $C_{p} (X)$ , if X contains a homeomorphic copy of the closed interval [0,1], real-valued maps which are everywhere discontinuous but continuous on all compact subsets of $C_{p} (X)$ .

Displaying similar documents to “Cobordisms of fold maps of 2k+2-manifolds into ℝ 3 k + 2 ”

Displaying similar documents to “Cobordisms of fold maps of 2k+2-manifolds into $ℝ^{3 k + 2}$ ”