On the second homology group of the Torelli subgroup of Aut(Fn)
| Autor: | Matthew B. Day, Andrew Putman |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Group (mathematics)
010102 general mathematics Geometric Topology (math.GT) Group Theory (math.GR) 16. Peace & justice Recursive form 01 natural sciences Surjective function Combinatorics Mathematics - Geometric Topology Mathematics::Group Theory Simple (abstract algebra) 0103 physical sciences FOS: Mathematics Generating set of a group Algebraic Topology (math.AT) Mathematics - Algebraic Topology 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematics - Group Theory Finite set Congruence subgroup Mathematics |
| Zdroj: | Geometry & Topology. 21:2851-2896 |
| ISSN: | 1364-0380 1465-3060 |
| DOI: | 10.2140/gt.2017.21.2851 |
| Popis: | Let IA_n be the Torelli subgroup of Aut(F_n). We give an explicit finite set of generators for H_2(IA_n) as a GL_n(Z)-module. Corollaries include a version of surjective representation stability for H_2(IA_n), the vanishing of the GL_n(Z)-coinvariants of H_2(IA_n), and the vanishing of the second rational homology group of the level l congruence subgroup of Aut(F_n). Our generating set is derived from a new group presentation for IA_n which is infinite but which has a simple recursive form. Comment: 39 pages; minor revision; to appear in Geom. Topol |
| Databáze: | OpenAIRE |
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