Vol. 5, No. 3, 2020

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Coassembly is a homotopy limit map

Cary Malkiewich and Mona Merling

Vol. 5 (2020), No. 3, 373–394
Abstract

We prove a claim by Williams that the coassembly map is a homotopy limit map. As an application, we show that the homotopy limit map for the coarse version of equivariant A-theory agrees with the coassembly map for bivariant A-theory that appears in the statement of the topological Riemann–Roch theorem.

In memory of Bruce Williams

Keywords
coassembly, $A$-theory, equivariant $A$-theory, homotopy limit, bivariant $A$-theory
Mathematical Subject Classification 2010
Primary: 19D10, 55P42, 55P91
Milestones
Received: 16 May 2019
Revised: 29 January 2020
Accepted: 15 February 2020
Published: 28 July 2020
Authors
Cary Malkiewich
Department of Mathematics
Binghamton University
Binghamton, NY
United States
Mona Merling
Department of Mathematics
University of Pennsylvania
Phialdelphia, PA
United States