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- W4310886256 abstract "In this article, we extend an argument of Vogtmann in order to show homology stability of the Euclidean orthogonal group $O_n(A)$ when $A$ is a valuation ring subject to arithmetic conditions on either its residue or its quotient field. In particular, it is shown that if $A$ is a henselian valuation ring, then the groups $O_n(A)$ exhibit homology stability if the residue field of $A$ has finite Pythagoras number. Our results include those of Vogtmann, and hold with various twisted coefficients. Using these results, we give analogues for fields $Fneqmathbb R$ of some computations that appear in the study of scissor congruences." @default.
- W4310886256 created "2022-12-20" @default.
- W4310886256 creator A5031882284 @default.
- W4310886256 date "2022-12-06" @default.
- W4310886256 modified "2023-09-24" @default.
- W4310886256 title "Twisted homology stability of O_n for valuation rings" @default.
- W4310886256 doi "https://doi.org/10.48550/arxiv.2212.03213" @default.
- W4310886256 hasPublicationYear "2022" @default.
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