Split injectivity of A-theoretic assembly maps

Abstract

We construct an equivariant coarse homology theory arising from the algebraic $K$-theory of spherical group rings and use this theory to derive split injectivity results for associated assembly maps. On the way, we prove that the fundamental structural theorems for Waldhausen's algebraic $K$-theory functor carry over to its nonconnective counterpart defined by Blumberg--Gepner--Tabuada.

arXiv comment41 pages

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Cited by in corpus (3)

• Topological equivariant coarse K-homology
• Cyclic homology for bornological coarse spaces
• Vanishing of Nil-terms and negative K-theory for additive categories