scholarly journals The General Kastler-Kalau-Walze Type Theorems About Witten Deformation

2022 ◽  
Author(s):  
Kaihua Bao ◽  
Xiaodong Shan ◽  
Yanhong Sun
Keyword(s):  
Witten Deformation

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 Witten deformation and the equivariant index

2008 ◽  
Vol 34 (3) ◽  
pp. 301-327
Author(s):  
Igor Prokhorenkov ◽  
Ken Richardson
Keyword(s):  
Equivariant Index ◽  
Witten Deformation

The Noncommutative Residue about Witten Deformation

2018 ◽  
Vol 35 (4) ◽  
pp. 550-568
Author(s):  
Kai Hua Bao ◽  
Ai Hui Sun ◽  
Chao Deng
Keyword(s):  
Noncommutative Residue ◽  
Witten Deformation

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 Novikov type inequalities for differential forms with non-isolated zeros

1997 ◽  
Vol 122 (2) ◽  
pp. 357-375 ◽  
Author(s):  
MAXIM BRAVERMAN ◽  
MICHAEL FARBER
Keyword(s):  
Critical Points ◽  
Differential Forms ◽  
Explicit Estimate ◽  
Morse Inequalities ◽  
De Rham Complex ◽  
Analytic Proof ◽  
Rham Complex ◽  
De Rham ◽  
Flat Bundle ◽  
Witten Deformation

We generalize the Novikov inequalities for 1-forms in two different directions: first, we allow non-isolated critical points (assuming that they are non-degenerate in the sense of R. Bott) and, secondly, we strengthen the inequalities by means of twisting by an arbitrary flat bundle. The proof uses Bismut's modification of the Witten deformation of the de Rham complex; it is based on an explicit estimate on the lower part of the spectrum of the corresponding Laplacian.In particular, we obtain a new analytic proof of the degenerate Morse inequalities of Bott.

scholarly journals Modified Novikov Operators and the Kastler-Kalau-Walze-Type Theorem for Manifolds with Boundary

2020 ◽  
Vol 2020 ◽  
pp. 1-28
Author(s):  
Sining Wei ◽  
Yong Wang
Keyword(s):  
Type Theorem ◽  
Compact Manifolds ◽  
Manifolds With Boundary ◽  
Spectral Action ◽  
Witten Deformation

In this paper, we give two Lichnerowicz-type formulas for modified Novikov operators. We prove Kastler-Kalau-Walze-type theorems for modified Novikov operators on compact manifolds with (respectively without) a boundary. We also compute the spectral action for Witten deformation on 4-dimensional compact manifolds.

Sign in / Sign up

Export Citation Format

Share Document