L2 Harmonic Forms on Noncompact Manifolds

2010 ◽  
pp. 249-254
Author(s):  
Robert J. Zimmer ◽  
Calvin C. Moore ◽  
Claude L. Schochet
Keyword(s):  
Harmonic Forms ◽  
Noncompact Manifolds

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 Hyper-Kähler Calabi metrics, L2 harmonic forms, resolved M2-branes, and AdS4/CFT3 correspondence

2001 ◽  
Vol 617 (1-3) ◽  
pp. 151-197 ◽  
Author(s):  
M. Cvetič ◽  
G.W. Gibbons ◽  
H. Lü ◽  
C.N. Pope
Keyword(s):  
Harmonic Forms

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 On products of harmonic forms

2001 ◽  
Vol 107 (3) ◽  
pp. 521-531 ◽  
Author(s):  
D. Kotschick
Keyword(s):  
Harmonic Forms

Supersymmetry on noncompact manifolds and complex geometry

1997 ◽  
Vol 85 (1) ◽  
pp. 1605-1618
Author(s):  
N. V. Borisov ◽  
K. N. Il'inskii
Keyword(s):  
Complex Geometry ◽  
Noncompact Manifolds

Spaces of embeddings of noncompact manifolds

2017 ◽  
Author(s):  
Assakta khalil ◽  
Abd Ghafur Bin Ahmad
Keyword(s):  
Noncompact Manifolds

scholarly journals Square integrable harmonic forms and representation theory

1998 ◽  
Vol 92 (3) ◽  
pp. 645-664 ◽  
Author(s):  
L. Barchini ◽  
R. Zierau
Keyword(s):  
Representation Theory ◽  
Harmonic Forms
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