Polynomially Bounded Cohomology and Virtually Nilpotent Groups
Speaker:
Sheagan John, Texas A&M University
Date and Time:
Friday, October 1, 2021 - 1:00pm to 2:00pm
Location:
Online
Abstract:
The application of cyclic cohomology to suitable dense subalgebras of C∗r(Γ) has proven to be an indispensable tool in obtaining information about structures which admit desirable Γ-actions. On manifolds satisfying π1(M)≅Γ, bounding cocyle growth rates is often crucial in proving the well-definedness of certain index theoretic secondary higher invariants. For Γ a virtually nilpotent group we show that every delocalized cyclic cocyle class admits a representative of polynomial growth; moreover, this result is extendable to the direct product of a virtually nilpotent group with a word hyperbolic group.