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September 2015 On homological stability for orthogonal and special orthogonal groups
Masayuki Nakada
Kyoto J. Math. 55(3): 627-640 (September 2015). DOI: 10.1215/21562261-3089109

Abstract

We shall prove that the map Hi(SOn(K),Z)Hi(SOn+1(K),Z) is bijective for 2i<n and surjective for 2in. Here K is an arbitrary Pythagorean field and the special orthogonal group SOn(K) is the subgroup of K-linear automorphisms over Kn with determinant one which preserve the Euclidean quadratic form q(x)=x12++xn2. It is derived from the homological stability of the orthogonal groups On(K) with twisted coefficients Zt.

Citation

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Masayuki Nakada. "On homological stability for orthogonal and special orthogonal groups." Kyoto J. Math. 55 (3) 627 - 640, September 2015. https://doi.org/10.1215/21562261-3089109

Information

Received: 31 January 2014; Revised: 11 July 2014; Accepted: 28 July 2014; Published: September 2015
First available in Project Euclid: 9 September 2015

zbMATH: 1330.20070
MathSciNet: MR3395983
Digital Object Identifier: 10.1215/21562261-3089109

Subjects:
Primary: 20J05

Keywords: group homology , homological stability , Scissors congruence

Rights: Copyright © 2015 Kyoto University

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Vol.55 • No. 3 • September 2015
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