Cellular chain complexes of universal covers of some 3-manifolds

Takefumi Nosaka

Cellular chain complexes of universal covers of some 3-manifolds

Geometric Topology 2022-02-23 v2 Algebraic Topology

Authors: Takefumi Nosaka

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

3-manifold universal cover cellular chain complex linking form dijkgraaf-witten invariant seifert manifold

Cite

@article{arxiv.2107.08851,
  title  = {Cellular chain complexes of universal covers of some 3-manifolds},
  author = {Takefumi Nosaka},
  journal= {arXiv preprint arXiv:2107.08851},
  year   = {2022}
}

Comments

14 pages. Comments are welcome. I made minor revisions. I added Section 2.2

Cellular chain complexes of universal covers of some 3-manifolds

Abstract

Keywords

Cite

Comments

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