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Abstract
Let M be a complex manifold of dimension n with smooth connected boundary X. Assume that M‾ admits a holomorphic S1-action preserving the boundary X and the S1-action is transversal on X. We show that the ∂‾-Neumann Laplacian on M is transversally elliptic and as a consequence, the m-th Fourier component of the q-th Dolbeault cohomology group Hm q(M‾) is finite dimensional, for every m∈Z and every q=0,1,…,n. This enables us to define ∑j=0 n(−1)jdimHm j(M‾) the m-th Fourier component of the Euler characteristic on M and to study large m-behavior of Hm q(M‾). In this paper, we establish an index formula for ∑j=0 n(−1)jdimHm j(M‾) and Morse inequalities for Hm q(M‾).
Original language | English |
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Article number | 108558 |
Journal | Journal of Functional Analysis |
Volume | 279 |
Issue number | 3 |
DOIs | |
State | Published - 15 Aug 2020 |
Keywords
- Index theorem
- Morse inequalities
- Pseudodifferential operators
- ∂‾-Neumann problem
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Dive into the research topics of 'S1-equivariant Index theorems and Morse inequalities on complex manifolds with boundary'. Together they form a unique fingerprint.Projects
- 2 Finished
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Analytic Torsion and Geometric Quantization on Complex and Cr Manifolds(2/2)
Huang, R.-T. (PI)
1/08/19 → 31/07/21
Project: Research
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A Study on Some Geometric Invariants on Manifolds(2/2)
Huang, R.-T. (PI)
1/08/17 → 31/07/18
Project: Research