A Bloch-Wigner complex for SL2

DOI10.1017/is013003031jkt13222zbMath1284.19003arXiv1107.0264OpenAlexW2962976788MaRDI QIDQ5397686

Kevin Hutchinson

Publication date: 24 February 2014

Published in: Journal of K-Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.0264

zbMATH Keywords

\(K\)-theoryBloch groupgroup homology

Mathematics Subject Classification ID

Homological methods in group theory (20J05) Symbols, presentations and stability of (K_2) (19C20) (K)-theory of forms (19G99)

Related Items (13)

The third homology of \(\mathrm{SL}_2(\mathbb{Q})\) ⋮ The homology of \(SL_2\) of discrete valuation rings ⋮ Homology of \(\operatorname{SL}_2\) over function fields. I: Parabolic subcomplexes ⋮ On the third homology of 𝑆𝐿₂ and weak homotopy invariance ⋮ Third homology of \(\mathrm{SL}_2\) over number fields: the norm-Euclidean quadratic imaginary case ⋮ A refined scissors congruence group and the third homology of \(\operatorname{SL}_2\) ⋮ The third homology of \(\mathrm{SL}_2\) of fields with discrete valuation ⋮ A Bloch-Wigner exact sequence over local rings ⋮ The reduced Dijkgraaf–Witten invariant of double twist knots in the Bloch group of 𝔽p ⋮ The third homology of \(\mathrm {SL}_2\) of local rings ⋮ On the low-dimensional homology of \(\mathrm{SL}_2(k [t, t^{- 1})\)] ⋮ The second homology of \(\mathrm{SL}_2\) of \(S\)-integers ⋮ The reduced Dijkgraaf–Witten invariant of twist knots in the Bloch group of a finite field

Cites Work

• Third homology of general linear groups
• The third homology of the special linear group of a field
• Torsion in \(K_ 2\) of fields
• Scissors congruences. II
• Special issues dedicated to Daniel Quillen on the occasion of his sixtieth birthday. Part I-III
• Homology of classical Lie groups made discrete. III
• Extended Bloch group and the Cheeger-Chern-Simons class
• On the powers of the fundamental ideal of a Witt ring
• Solution to the presentation problem for powers of the augmentation ideal of torsion free and torsion Abelian groups.
• A new approach to Matsumoto's theorem
• The extended Bloch group and the Cheeger-Chern-Simons class
• On the cohomology and K-theory of the general linear groups over a finite field
• The indecomposable $K_3$ of fields
• Sur les sous-groupes arithmétiques des groupes semi-simples déployés

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