Abstract
We introduce the notion of a v-summable Fredholm module over a locally convex dg algebra omega and construct its Chern character as a cocycle on the entire cyclic complex of omega, extending the construction of Jaffe, Lesniewski and Osterwalder to a differential graded setting. Using this Chern character, we prove an index theorem involving an abstract version of a Bismut-Chern character ...
Abstract
We introduce the notion of a v-summable Fredholm module over a locally convex dg algebra omega and construct its Chern character as a cocycle on the entire cyclic complex of omega, extending the construction of Jaffe, Lesniewski and Osterwalder to a differential graded setting. Using this Chern character, we prove an index theorem involving an abstract version of a Bismut-Chern character constructed by Getzler, Jones and Petrack in the context of loop spaces. Our theory leads to a rigorous construction of the path integral for N = 1/2 supersymmetry which satisfies a DuistermaatHeckman type localization formula on loop space.(C) 2021 Elsevier Inc. All rights reserved.
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