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Witten deformation using Lie groupoids.
- Source :
-
Advances in Mathematics . Mar2022, Vol. 398, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- We express Witten's deformation of Morse functions using deformation to the normal cone and C ⁎ -modules. This allows us to obtain asymptotics of the 'large eigenvalues'. This is then applied to the case of Morse-Bott functions inspired by [2]. Our methods extend to Morse functions along a foliation. We construct the Witten deformation using any generic function on an arbitrary foliation on a compact manifold and establish the compactness of its resolvent. When the foliation has a holonomy invariant transverse measure we show that our result implies Morse inequalities obtained by Connes and Fack [10] in a slightly more general situation. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FOLIATIONS (Mathematics)
*MORSE theory
*INVARIANT measures
*GROUPOIDS
*EIGENVALUES
Subjects
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 398
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 155559966
- Full Text :
- https://doi.org/10.1016/j.aim.2021.108142