Split injectivity of A-theoretic assembly maps

Bunke, Ulrich; Kasprowski, Daniel; Winges, Christoph

doi:10.1093/imrn/rnz209

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Split injectivity of A-theoretic assembly maps

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Winges, Christoph
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1093/imrn/rnz209
(Publisher version)

https://doi.org/10.48550/arXiv.1811.11864
(Preprint)

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Citation

Bunke, U., Kasprowski, D., & Winges, C. (2021). Split injectivity of A-theoretic assembly maps. International Mathematics Research Notices, 2021(2), 885-947. doi:10.1093/imrn/rnz209.

Cite as: https://hdl.handle.net/21.11116/0000-0007-7558-3

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.