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Title:
Index theory on manifolds with fibered boundaries and its applications
Speaker:
Abstract:
Noncommutative geometry has provided a great extension of Atiyah-Singer index theory, for example index theory for foliations and higher index theory for covering spaces. It is known that many of such constructions can be nicely explained using Lie groupoids and KK theory for the associated C*-algebras. In this talk, I will focus on index theory for manifolds with fibered boundaries. An analytic approach to elliptic theory on such spaces was started by Mazzeo and Melrose, and later the corresponding groupoids were constructed. I wlii explain my work to give a topological approach to index theory on such spaces using groupoids and noncommutative geometric ideas. I will also explain two applications, localization problem for signatures on singular fiber bundles and signatures on Witt spaces.
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