Geodesic
On finite derived quotients of 3–manifold groups
Cavendish, Will1
1McKinsey and Company, 110 Charles Street, Toronto ON, M5S 1K9, Canada
Algebraic and Geometric Topology, Tome 15 (2015) no. 6, pp. 3355-3369
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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 G≅π1(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 → ℚ∕ℤ.

DOI : 10.2140/agt.2015.15.3355
Classification : 57M10, 57M60
Keywords: finite sheeted covering spaces, 3–manifolds, first Betti number, linking pairing

Cavendish, Will  1

1 McKinsey and Company, 110 Charles Street, Toronto ON, M5S 1K9, Canada 
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Cavendish, Will. On finite derived quotients of 3–manifold groups. Algebraic and Geometric Topology, Tome 15 (2015) no. 6, pp. 3355-3369. doi: 10.2140/agt.2015.15.3355

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