Corpus ID: 119135457

Heat kernel asymptotics, local index theorem and trace integrals for CR manifolds with $S^1$ action

@article{Cheng2015HeatKA,
  title={Heat kernel asymptotics, local index theorem and trace integrals for CR manifolds with \$S^1\$ action},
  author={Jih-Hsin Cheng and Chin-Yu Hsiao and I Hsun Tsai},
  journal={arXiv: Differential Geometry},
  year={2015}
}
Among those transversally elliptic operators initiated by Atiyah and Singer, Kohn's $\Box_b$ operator on CR manifolds with $S^1$ action is a natural one of geometric significance for complex analysts. Our first main result establishes an asymptotic expansion for the heat kernel of such an operator with values in its Fourier components, which involves an unprecedented contribution in terms of a distance function from lower dimensional strata of the $S^1$-action. Our second main result computes a… Expand
5 Citations
A Local Index Theorem of Transversal Type on Manifolds with Locally Free $\mathbb{S}^1$-action
We study an index of a transversal Dirac operator on an odd-dimensional manifold $X$ with locally free $\mathbb{S}^1$-action. One difficulty of using heat kernel method lies in the understanding ofExpand
A LOCAL INDEX THEOREM OF TRANSVERSAL TYPE ON MANIFOLDS WITH LOCALLY FREE S-ACTION
We study an index of a transversal Dirac operator on an odd-dimensional manifold X with locally free S-action. One difficulty of using heat kernel method lies in the understanding of the asymptoticExpand
S1-equivariant Index theorems and Morse inequalities on complex manifolds with boundary
Abstract Let M be a complex manifold of dimension n with smooth connected boundary X. Assume that M ‾ admits a holomorphic S 1 -action preserving the boundary X and the S 1 -action is transversal onExpand
Szegö kernel asymptotic expansion on strongly pseudoconvex CR manifolds with S1 action
Let [Formula: see text] be a compact connected strongly pseudoconvex Cauchy–Riemann (CR) manifold of real dimension [Formula: see text] with a transversal CR [Formula: see text] action on [Formula:Expand
On the stability of equivariant embedding of compact CR manifolds with circle action
We prove the stability of the equivariant embedding of compact strictly pseudoconvex CR manifolds with transversal CR circle action under circle invariant deformations of the CR structures.

References

SHOWING 1-10 OF 49 REFERENCES
Heat Kernels and Dirac Operators
The past few years have seen the emergence of new insights into the Atiyah-Singer Index Theorem for Dirac operators. In this book, elementary proofs of this theorem, and some of its more recentExpand
The Atiyah-Singer index formula for subelliptic operators on contact manifolds. Part I
The Atiyah-Singer index theorem gives a topological formula for the index of an elliptic differential operator. The topological index depends on a cohomology class that is constructed from theExpand
Traces of heat operators on Riemannian foliations
We consider the basic heat operator on functions on a Riemannian foliation of a compact, Riemannian manifold, and we show that the trace K B (t) of this operator has a particular asymptotic expansionExpand
Almost CR quantization via the index of transversally elliptic Dirac operators
Almost CR quantization via the index of transversally elliptic Dirac operators Daniel Sean Fitzpatrick Doctor of Philosophy Graduate Department of Mathematics University of Toronto 2009 Let M be aExpand
The asymptotics of heat kernels on Riemannian foliations
Abstract. We study the basic Laplacian of a Riemannian foliation on a compact manifold M by comparing it to the induced Laplacian on the basic manifold. We show that the basic heat kernel onExpand
Asymptotic expansion of the heat kernel for orbifolds
We study the relationship between the geometry and the Laplace spectrum of a Riemannian orbifoldO via its heat kernel; as in the manifold case, the time-zero asymptotic expansion of the heat kernelExpand
The signature theorem for V-manifolds
Here L(g, M) is the equivariant L-class defined by Atiyah_Singer[4]. By choosing suitable metrics and connections, we can express L(g, M) in differential forms. These characteristic forms are definedExpand
The equivariant index theorem for transversally elliptic operators and the basic index theorem for Riemannian foliations
In this expository paper, we explain a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a $G$-manifold. The formula is a sum of integrals over blowupsExpand
Subelliptic Spin C Dirac operators, I
Let X be a compact Kahler manifold with strictly pseudoconvex bound- ary, Y. In this setting, the SpinC Dirac operator is canonically identified with ¯ ∂ + ¯ ∂ ∗ : C ∞ (X ;Λ 0,e ) →C ∞ (X ;Λ 0,o ).Expand
On the variation in the cohomology of the symplectic form of the reduced phase space
is called the momentum mapping of the Hamiltonian T-action. Given (1.1), the condition (1.2) just means that T acts along the fibers of J. For the basic definitions and properties of non-commutativeExpand
...
1
2
3
4
5
...