## Cellular Chain Complexes of Universal Covers of Some 3-Manifolds

J. Math. Sci. Univ. Tokyo
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 $S^3$, some cyclic branched cover of $S^3$, and some Seifert manifolds. In application, we establish a formula for calculating the linking form of a cyclic branched cover of $S^3$, 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.