## 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
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.