On the cohomology of SL$_n(\mathbb{Z})$

Avner Ash

paper

On the cohomology of SL $_{n} (Z)$

arXiv:2402.08840

Abstract

Let St denote the Steinberg module of $S L_{n} (Q)$ tensored with Q. Let Sh denote the sharbly resolution of St. By Borel-Serre duality, $H^{n (n - 1) /2 - i} (S L_{n} (Z), Q)$ is isomorphic to $H_{i} (S L_{n} (Z), S t)$ . The latter is isomorphic to the homology of the $S L_{n} (Z)$ -coinvariants of Sh. We produce nonzero classes in $H_{i} (S L_{n} (Z), S t)$ for certain small $i$ in terms of sharbly cycles and cosharbly cocycles.

arXiv comment17 pages

On the cohomology of SLn​(Z)

Abstract

On the cohomology of SL $_{n} (Z)$