- Patodi - Singer Index Theorem ∗
نویسنده
چکیده
In [Wu], the noncommutative Atiyah-Patodi-Singer index theorem was proved. In this paper, we extend this theorem to the equivariant case.
منابع مشابه
v 1 [ m at h . D G ] 2 5 M ar 1 99 9 Real embeddings and the Atiyah - Patodi - Singer index theorem for Dirac operators ∗
We present the details of our embedding proof, which was announced in [DZ1], of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary [APS1]. Introduction The index theorem of Atiyah, Patodi and Singer [APS1, (4.3)] for Dirac operators on manifolds with boundary has played important roles in various problems in geometry, topology as well as mathematical physics. ...
متن کاملJ. Differential Geometry Families of Dirac Operators, Boundaries and the B-calculus
A version of the Atiyah Patodi Singer index theorem is proved for general families of Dirac operators on compact manifolds with boundary The van ishing of the analytic index of the boundary family inK of the base allows us to de ne through an explicit trivialization a smooth family of bound ary conditions of generalized Atiyah Patodi Singer type The calculus of b pseudodi erential operators is ...
متن کاملar X iv : h ep - t h / 99 08 13 8 v 1 2 0 A ug 1 99 9 On The Arnold Conjecture And The Atiyah - Patodi - Singer Index Theorem
The Arnold conjecture yields a lower bound to the number of periodic classical trajectories in a Hamiltonian system. Here we count these trajectories with the help of a path integral, which we inspect using properties of the spectral flow of a Dirac operator in the background of a Sp(2N) valued gauge field. We compute the spectral flow from the Atiyah-Patodi-Singer index theorem, and apply the ...
متن کاملar X iv : h ep - t h / 99 08 13 8 v 2 2 5 A ug 1 99 9 On The Arnold Conjecture And The Atiyah - Patodi - Singer Index Theorem
The Arnold conjecture yields a lower bound to the number of periodic classical trajectories in a Hamiltonian system. Here we count these trajectories with the help of a path integral, which we inspect using properties of the spectral flow of a Dirac operator in the background of a Sp(2N) valued gauge field. We compute the spectral flow from the Atiyah-Patodi-Singer index theorem, and apply the ...
متن کاملThe Index of Dirac Operators on Incomplete Edge Spaces
We derive a formula for the index of a Dirac operator on an incomplete edge space satisfying a “geometric Witt condition.” We accomplish this by cutting off to a smooth manifold with boundary, applying the Atiyah-Patodi-Singer index theorem, and taking a limit. We deduce corollaries related to the existence of positive scalar curvature metrics on incomplete edge spaces.
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