English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The main result of this paper is the $G$-homotopy invariance of the $G$-indexof signature operator of proper co-compact $G$-manifolds. If proper co-compact$G$ manifolds $X$ and $Y$ are $G$-homotopy equivalent, then we prove that theimages of their signature operators by the $G$-index map are the same in the$K$-theory of the $C^{*}$-algebra of the group $G$. Neither discreteness of thelocally compact group $G$ nor freeness of the action of $G$ on $X$ arerequired, so this is a generalization of the classical case of closedmanifolds. Using this result we can deduce the equivariant version of Novikovconjecture for proper co-compact $G$-manifolds from the Strong Novikovconjecture for $G$.

$G$-Homotopy Invariance of the Analytic Signature of Proper Co-compact $G$-manifolds and Equivariant Novikov Conjecture