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A cyclic cocycle and relative index theorems on partitioned manifolds

Published 10 May 2017 in math.DG and math.KT | (1705.03732v2)

Abstract: In this paper, we extend Roe's cyclic $1$-cocycle to relative settings. We also prove two relative index theorems for partitioned manifolds by using its cyclic cocycle, which are generalizations of index theorems on partitioned manifolds. One of these theorems is a variant of [M. Karami-A.H.S. Sadegh-M.E. Zadeh, arXiv:1411.6090, Theorem 3.3].

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