The Chern character of ϑ-summable C_q-Fredholm modules over locally convex differential graded algebras

2023/12/02 by Jonas Miehe, Miehe, Jonas · 1 voice
Mathematics · #19D55 (Secondary) #58B34 (Primary) 46L87 #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT

paper · pdf · doi:10.48550/arxiv.2312.01106

arxiv published 2023/12/02 · arxiv updated 2023/12/11

Abstract

Let Ω be a locally convex differential graded algebra. We introduce the Chern character of ϑ-summable C_q-Fredholm modules over Ω, generalizing the JLO cocycle to the differential graded setting. This allows treating the case of even ϑ-summable Fredholm modules over Ω (which has been previously considered by Güneysu/Ludewig in the context of localization on loop spaces) and odd ϑ-summable Fredholm modules over Ω simultaneously. We prove all naturally expected properties of this construction and relate it to the spectral flow in the odd case.

Discussions

• Jonas Miehe The Chern character of $\vartheta$-summable $\mathcal{C}_q$-Fredholm modules over locally convex differential graded algebras. (arXiv:2312.01106v1 [math.KT]) http://arxiv.org/abs/2312.0110 [bsky, 0 points, 0 comments]

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