Cellular Chain Complexes of Universal Covers of Some 3-Manifolds
Vol. 29 (2022), No. 1, Page 89-113.
Nosaka, Takefumi
Cellular Chain Complexes of Universal Covers of Some 3-Manifolds
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Abstract:
For a closed 3-manifold M in a certain class, we give a presentation of the cellular chain complex of the universal cover of M. The class includes all surface bundles, some surgeries of knots in S3, some cyclic branched cover of S3, and some Seifert manifolds. In application, we establish a formula for calculating the linking form of a cyclic branched cover of S3, and develop procedures of computing some Dijkgraaf-Witten invariants.
Keywords: Universal covering, 3-manifold group, group homology, knot, branched coverings, linking form.
Mathematics Subject Classification (2010): 57M10, 58K65, 57N60, 55N45.
Mathematical Reviews Number: MR4414248
Received: 2021-08-20