scholarly journals Morse Inequalities and Embeddings for CR Manifolds with Circle Action

2020 ◽  
Vol 15 (2) ◽  
Author(s):  
Hendrik Herrmann ◽  
Xiaoshan Li
Keyword(s):  
Circle Action ◽  
Morse Inequalities ◽  
Cr Manifolds

scholarly journals Szegö kernel asymptotics and Morse inequalities on CR manifolds

2011 ◽  
Vol 271 (1-2) ◽  
pp. 509-553 ◽  
Author(s):  
Chin-Yu Hsiao ◽  
George Marinescu
Keyword(s):  
Morse Inequalities ◽  
Cr Manifolds ◽  
Szegö Kernel ◽  
Szegő Kernel ◽  
Szego Kernel

scholarly journals On the stability of equivariant embedding of compact CR manifolds with circle action

2017 ◽  
Vol 289 (1-2) ◽  
pp. 201-222 ◽  
Author(s):  
Chin-Yu Hsiao ◽  
Xiaoshan Li ◽  
George Marinescu
Keyword(s):  
Circle Action ◽  
Cr Manifolds ◽  
Equivariant Embedding ◽  
The Stability

scholarly journals Equivariant Kodaira Embedding for CR Manifolds with Circle Action

2020 ◽  
Author(s):  
Chin-Yu Hsiao ◽  
Xiaoshan Li ◽  
George Marinescu
Keyword(s):  
Circle Action ◽  
Cr Manifolds

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.

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