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A cyclic cocycle and relative index theorems on partitioned manifolds
Tatsuki Seto
In this paper, we extend Roe's cyclic -cocycle to relative settings. We also prove two relative index theorems for partitioned manifolds by using its cyclic cocycle, which are g…
A note on Atiyah's -index theorem in Heisenberg calculus
Tatsuki Seto
In this note, we prove an index theorem on Galois covering for Heisenberg elliptic differential operators, which is not elliptic, analogous to Atiyah's -index theorem. This note…
Toeplitz operators and the Roe-Higson type index theorem
Tatsuki Seto
Let be a complete Riemannian manifold and assume that is partitioned by a hypersurface . In this paper we introduce a novel class of functions on non…
Toeplitz operators and the Roe-Higson type index theorem in Riemannian surfaces
Tatsuki Seto
We study a two dimensional analogue of the Roe-Higson index theorem for a partitioned manifold. We prove that Connes' pairing of some invertible element with Roe's cyclic one-cocyc…