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- W4297804153 abstract "Controlled topology is one of the main tools for proving the isomorphism conjecture concerning the algebraic $K$-theory of group rings. In this article we dive into this machinery in two examples: when the group is infinite cyclic and when it is the infinite dihedral group - in both cases with the family of finite subgroups. We prove a vanishing theorem and show how to explicitly squeeze the generators of these groups in $K_1$. For the infinite cyclic group, when taking coefficients in a regular ring, we get a squeezing result for every element of $K_1$; this follows from the well-known result of Bass, Heller and Swan." @default.
- W4297804153 created "2022-10-01" @default.
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- W4297804153 date "2019-07-13" @default.
- W4297804153 modified "2023-09-25" @default.
- W4297804153 title "Two examples of vanishing and squeezing in $K_1$" @default.
- W4297804153 doi "https://doi.org/10.48550/arxiv.1907.06135" @default.
- W4297804153 hasPublicationYear "2019" @default.
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