Dirac operators on non-compact orbifolds
نویسندگان
چکیده
منابع مشابه
Index Theory of Equivariant Dirac Operators on Non-compact Manifolds
We define a regularized version of an equivariant index of a (generalized) Dirac operator on a non-compact complete Riemannian manifold M acted on by a compact Lie group G. Our definition requires an additional data – an equivariant map v : M → g = LieG, such that the corresponding vector field on M does not vanish outside of a compact subset. For the case when M = C and G is the circle group a...
متن کاملIndex Theorem for Equivariant Dirac Operators on Non-compact Manifolds
Let D be a (generalized) Dirac operator on a non-compact complete Riemannian manifold M acted on by a compact Lie group G. Let v : M → g = LieG be an equivariant map, such that the corresponding vector field on M does not vanish outside of a compact subset. These data define an element of K-theory of the transversal cotangent bundle to M . Hence, by embedding of M into a compact manifold, one c...
متن کاملDifferential operators on orbifolds
An algorithm is presented that computes explicit generators for the ring of differential operators on an orbifold, the quotient of a complex vector space by a finite group action. The algorithm also describes the relations among these generators. The algorithm presented in this paper is based on Schwarz’s study of a map carrying invariant operators to operators on the orbifold and on an algorit...
متن کاملThe Spectrum of Twisted Dirac Operators on Compact Flat Manifolds
Let M be an orientable compact flat Riemannian manifold endowed with a spin structure. In this paper we determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles of M , and we derive a formula for the corresponding eta series. In the case of manifolds with holonomy group Z2 , we give a very simple expression for the multiplicities of eigenvalues that allows t...
متن کاملDirac Operators for Coadjoint Orbits of Compact Lie Groups
The coadjoint orbits of compact Lie groups carry many Kähler structures, which include a Riemannian metric and a complex structure. We provide a fairly explicit formula for the Levi–Civita connection of the Riemannian metric, and we use the complex structure to give a fairly explicit construction of the Dirac operator for the Riemannian metric, in a way that avoids use of the spin groups. Subst...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2009
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2008.10.010