Journal of Noncommutative Geometry


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Volume 10, Issue 1, 2016, pp. 379–404
DOI: 10.4171/JNCG/236

Published online: 2016-03-22

The noncommutative infinitesimal equivariant index formula, Part II

Yong Wang[1]

(1) Northeast Normal University, Changchun, Jilin, China

In this paper, we prove that infinitesimal equivariant Chern–Connes characters are well defined. We decompose an equivariant index as a pairing of infinitesimal equivariant Chern–Connes characters with the Chern character of an idempotent matrix. We compute the limit of infinitesimal equivariant Chern–Connes characters when the time goes to zero by using the Getzler symbol calculus and then extend these theorems to the family case. We also prove that infinitesimal equivariant eta cochains are well defined and prove the noncommutative infinitesimal equivariant index formula for manifolds with boundary.

Keywords: Infinitesimal equivariant Chern–Connes characters, Getzler symbol calculus, infinitesimal equivariant eta cochains, infinitesimal equivariant family Chern–Connes characters

Wang Yong: The noncommutative infinitesimal equivariant index formula, Part II. J. Noncommut. Geom. 10 (2016), 379-404. doi: 10.4171/JNCG/236