Noncommutative Geometry Seminar

Date: December 2, 2020

Time: 1:00PM - 2:00PM

Location: Zoom 942810031

Speaker: Sheagan John, Texas A&M University

Title: Pairing of Secondary Higher Invariants and Cyclic Cohomology for Virtually Nilpotent Groups

Abstract: We prove that if G is a virtually nilpotent group, then each delocalized cyclic cocycle on the group algebra has a representative of polynomial growth. For each delocalized cyclic cocyle we thus define a higher analogue of Lott’s delocalized eta invariant and prove its convergence for invertible differential operators. We also use a determinant map construction of Xie and Yu to prove that if G is of polynomial growth then there is a well defined pairing between delocalized cyclic cocyles and K-theory classes of C*-algebraic secondary higher invariants. When this K-theory class is that of a higher rho invariant of an invertible differential operator we show this pairing is precisely the aforementioned higher analogue of Lott’s delocalized eta invariant.

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