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The
codimension-one cohomology of $\mathrm{SL}_n \mathbb{Z}$
Thomas Church and Andrew Putman |
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Geometry & Topology 21 (2017) 999–1032
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Abstract |
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We prove that , where is the cohomological dimension of , and similarly for . We also prove analogous vanishing theorems for cohomology with coefficients in a rational representation of the algebraic group . These theorems are derived from a presentation of the Steinberg module for whose generators are integral apartment classes, generalizing Manin’s presentation for the Steinberg module of . This presentation was originally constructed by Bykovskiĭ. We give a new topological proof of it. |
Keywords
cohomology of arithmetic groups, Steinberg module, partial
bases
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Mathematical Subject Classification 2010
Primary: 11F75
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References |
Publication
Received: 4 August 2015
Revised: 17 April 2016
Accepted: 13 July 2016
Published: 17 March 2017
Proposed: Ronald Stern
Seconded: Mark Behrens, András I. Stipsicz
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Authors |
| Thomas Church | |
| Department of Mathematics Stanford University 450 Serra Mall Stanford, CA 94305 United States |
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| http://math.stanford.edu/~church/ | |
| Andrew Putman | |
| Department of Mathematics University of Notre Dame 255 Hurley Notre Dame, IN 46556 United States |
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| http://www3.nd.edu/~andyp/ | |
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