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10 papers · 1 filter
A global view of equivariant vector bundles and Dirac operators on some compact homogeneous spaces
Marc A. Rieffel
In order to facilitate the comparison of Riemannian homogeneous spaces of compact Lie groups with noncommutative geometries ("quantizations") that approximate them, we develop here…
Elliptic Genera, Transgression and Loop Space Chern-Simons Forms
Qingtao Chen, Fei Han
We compute the Chern-Simons transgressed forms of some modularly invariant characteristic forms, which are related to the elliptic genera. We study the modularity properties of the…
The Boundary between Compact and Noncompact Complete Riemann Manifolds
D. Holcman, C. Pugh
In 1941 Sumner Myers proved that if the Ricci curvature of a complete Riemann manifold has a positive infimum then the manifold is compact and its diameter is bounded in terms of t…
The equivariant cohomology of hypertoric varieties and their real loci
Megumi Harada, Tara S. Holm
Let M be a Hamiltonian T space with a proper moment map, bounded below in some component. In this setting, we give a combinatorial description of the T-equivariant cohomology of M,…
Contact reduction and groupoid actions
Marco Zambon, Chenchang Zhu
We introduce a new method to perform reduction of contact manifolds that extends Willett's (math.SG/0104080) and Albert's results. To carry out our reduction procedure all we need…
Integrating Lie algebroids via stacks
Hsian-Hua Tseng, Chenchang Zhu
Lie algebroids can not always be integrated into Lie groupoids. We introduce a new object--``Weinstein groupoid'', which is a differentiable stack with groupoid-like axioms. With i…