TY - JOUR

T1 - The integral homology of orientable Seifert manifolds

AU - Bryden, J.

AU - Lawson, T.

AU - Pigott, B.

AU - Zvengrowski, P.

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2003/1/1

Y1 - 2003/1/1

N2 - For any orientable Seifert manifold M, the integral homology group H1(M)=H1(M;ℤ) is computed and explicit generators are found. This calculation gives a presentation for the p-torsion of H1(M) for any prime p. Since Seifert manifolds have dimension 3, H1(M) determines H*(M;A) and H*(M;A) as well, for any abelian group A. The complete details are given when A=ℤ, ℤ/ps.In order to calculate the partition functions of the Dijkgraaf-Witten topological quantum field theories it is necessary to compute the linking form of the underlying 3-manifold. In the case of the orientable Seifert manifolds it is possible to compute the linking form. The calculation of the linking form involves finding a presentation of the torsion of the first integral homology of the orientable Seifert manifolds, which is the main result of this paper.

AB - For any orientable Seifert manifold M, the integral homology group H1(M)=H1(M;ℤ) is computed and explicit generators are found. This calculation gives a presentation for the p-torsion of H1(M) for any prime p. Since Seifert manifolds have dimension 3, H1(M) determines H*(M;A) and H*(M;A) as well, for any abelian group A. The complete details are given when A=ℤ, ℤ/ps.In order to calculate the partition functions of the Dijkgraaf-Witten topological quantum field theories it is necessary to compute the linking form of the underlying 3-manifold. In the case of the orientable Seifert manifolds it is possible to compute the linking form. The calculation of the linking form involves finding a presentation of the torsion of the first integral homology of the orientable Seifert manifolds, which is the main result of this paper.

KW - Seifert manifolds

KW - p-component

UR - http://www.scopus.com/inward/record.url?scp=0038498826&partnerID=8YFLogxK

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U2 - 10.1016/S0166-8641(02)00062-7

DO - 10.1016/S0166-8641(02)00062-7

M3 - Article

AN - SCOPUS:0038498826

VL - 127

SP - 259

EP - 275

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 1-2

ER -