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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On finite derived quotients of $3$–manifold groups

Will Cavendish

Algebraic & Geometric Topology 15 (2015) 3355–3369
Abstract

This paper studies the set of finite groups appearing as π1(M)π1(M)(n), where M is a closed, orientable 3–manifold and π1(M)(n) denotes the nth term of the derived series of π1(M). Our main result is that if M is a closed, orientable 3–manifold, n 2, and Gπ1(M)π1(M)(n) is finite, then the cup-product pairing H2(G) H2(G) H4(G) has cyclic image C, and the pairing H2(G) H2(G)C is isomorphic to the linking pairing H1(M) Tors H1(M) Tors .

Keywords
finite sheeted covering spaces, 3–manifolds, first Betti number, linking pairing
Mathematical Subject Classification 2010
Primary: 57M10
Secondary: 57M60
References
Publication
Received: 30 July 2014
Revised: 13 April 2015
Accepted: 13 April 2015
Published: 12 January 2016
Authors
Will Cavendish
McKinsey and Company
110 Charles Street
Toronto ON, M5S 1K9
Canada