Low-dimensional Homology of SL₂(k[t,1/t])

2014/04/23 by Kevin Hutchinson-Lhuissier, Kevin Hutchinson, Hutchinson, Kevin
Mathematics · #20G10 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT #msc:20G10

paper · pdf · doi:10.48550/arxiv.1404.5896

24 pages

arxiv created 2014/04/23 · openalex publication_date 2014/04/23 · arxiv updated 2014/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We prove analogues of the fundamental theorem of algebraic K-theory for the second and third homology of SL₂ over an infinite field k. The statements involve Milnor-Witt K-theory and scissors congruence groups. We use these results to calculate the low-dimensional homology of SL₂ of Laurent polynomials over certain fields.

Citations

• The third homology of SL₂ of local rings

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