63 research outputs found
A Positive Mass Theorem for Spaces with Asymptotic SUSY Compactification
We prove a positive mass theorem for spaces which asymptotically approach a
flat Euclidean space times a Calabi-Yau manifold (or any special honolomy
manifold except the quaternionic K\"ahler). This is motivated by the very
recent work of Hertog-Horowitz-Maeda.Comment: To appear in CM
Hitchin-Thorpe Inequality for Noncompact Einstein 4-Manifolds
We prove a Hitchin-Thorpe inequality for noncompact Einstein 4-manifolds with
asymptotic geometry at infinity. The asymptotic geometry at infinity is either
a cusp bundle over a compact space (the fibered cusps) or a fiber bundle over a
cone with a compact fiber (the fibered boundary). Many noncompact Einstein
manifolds come with such a geometry at infinity.Comment: 17 page
An Index Theorem for Toeplitz Operators on Odd Dimensional Manifolds with Boundary
We establish an index theorem for Toeplitz operators on odd dimensional spin
manifolds with boundary. It may be thought of as an odd dimensional analogue of
the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with
boundary. In particular, there occurs naturally an invariant of type
associated to representatives on even dimensional manifolds, which should
be of independent interests. For example, it gives an intrinsic interpretation
of the so called Wess-Zumino term in the WZW theory in physics.Comment: Completely revised. A gap in the proof fixed. To appear in JF
The Intersection R-Torsion for Finite Cone
We prove a formula for the intersection R-torsion of a finite cone and use it
to introduce a family of spectral invariants which is closely related to
Cheeger's half torsion.Comment: introduction revise
- …