Comparison between two complexes on a singular space

2017 ◽  
Vol 2017 (724) ◽  
pp. 1-52 ◽  
Author(s):  
Ursula Ludwig
Keyword(s):  
Stratified Spaces ◽  
Morse Functions ◽  
Singular Space ◽  
Witten Deformation

AbstractIn this article we generalise the Witten deformation for stratified spaces and a class of Morse functions which we call radial Morse functions. In the first part of the article we perform the Witten deformation on the complex of

scholarly journals AN ANALYTIC APPROACH TO THE STRATIFIED MORSE INEQUALITIES FOR COMPLEX CONES

2013 ◽  
Vol 24 (12) ◽  
pp. 1350100
Author(s):  
URSULA LUDWIG
Keyword(s):  
Morse Theory ◽  
Singular Points ◽  
Analytic Approach ◽  
Morse Inequalities ◽  
Singular Spaces ◽  
Analytic Proof ◽  
Morse Functions ◽  
Complex Cone ◽  
Witten Deformation

In a previous paper the author extended the Witten deformation to singular spaces with cone-like singularities and to a class of Morse functions called admissible Morse functions. The method applies in particular to complex cones and stratified Morse functions in the sense of the theory developed by Goresky and MacPherson. It is well-known from stratified Morse theory that the singular points of the complex cone contribute to the stratified Morse inequalities in middle degree only. In this paper, an analytic proof of this fact is given.

scholarly journals Harmonic forms and cohomology of singular stratified spaces

2007 ◽  
Vol 131 (5) ◽  
pp. 422-456
Author(s):  
Vincenzo Ancona ◽  
Bernard Gaveau ◽  
Masami Okada
Keyword(s):  
Harmonic Forms ◽  
Stratified Spaces

scholarly journals Morse functions on cobordisms

2011 ◽  
Vol 63 (1) ◽  
pp. 146-157
Author(s):  
V. V. Sharko
Keyword(s):  
Morse Functions

scholarly journals Orbispaces as differentiable stratified spaces

2017 ◽  
Vol 108 (3) ◽  
pp. 805-859 ◽  
Author(s):  
Marius Crainic ◽  
João Nuno Mestre
Keyword(s):  
Stratified Spaces

scholarly journals WITTEN DEFORMATION FOR NONCOMPACT MANIFOLDS WITH BOUNDED GEOMETRY

2021 ◽  
pp. 1-38
Author(s):  
Xianzhe Dai ◽  
Junrong Yan
Keyword(s):  
Essential Role ◽  
Morse Function ◽  
Noncompact Manifold ◽  
Morse Inequalities ◽  
Bounded Geometry ◽  
Noncompact Manifolds ◽  
Witten Laplacian ◽  
Relative Cohomology ◽  
Witten Deformation ◽  
Small Eigenvalues

Abstract Motivated by the Landau–Ginzburg model, we study the Witten deformation on a noncompact manifold with bounded geometry, together with some tameness condition on the growth of the Morse function f near infinity. We prove that the cohomology of the Witten deformation $d_{Tf}$ acting on the complex of smooth $L^2$ forms is isomorphic to the cohomology of the Thom–Smale complex of f as well as the relative cohomology of a certain pair $(M, U)$ for sufficiently large T. We establish an Agmon estimate for eigenforms of the Witten Laplacian which plays an essential role in identifying these cohomologies via Witten’s instanton complex, defined in terms of eigenspaces of the Witten Laplacian for small eigenvalues. As an application, we obtain the strong Morse inequalities in this setting.

scholarly journals The stratified spaces of a symplectic lie group action

2006 ◽  
Vol 58 (1) ◽  
pp. 51-75 ◽  
Author(s):  
Juan-Pablo Ortega ◽  
Tudor S. Ratiu
Keyword(s):  
Group Action ◽  
Lie Group ◽  
Stratified Spaces ◽  
Lie Group Action

scholarly journals Tight complexes in 3-space admit perfect discrete Morse functions

2015 ◽  
Vol 45 ◽  
pp. 71-84 ◽  
Author(s):  
Karim Adiprasito ◽  
Bruno Benedetti
Keyword(s):  
Morse Functions

scholarly journals Strings in Singular Space-Times and Their Universal Gauge Theory

2017 ◽  
Vol 18 (8) ◽  
pp. 2641-2692 ◽  
Author(s):  
Athanasios Chatzistavrakidis ◽  
Andreas Deser ◽  
Larisa Jonke ◽  
Thomas Strobl
Keyword(s):  
Gauge Theory ◽  
Singular Space
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