The Alexander polynomial as an intersection of two cycles in a symmetric power

Nikita Kalinin

doi:10.1142/S0218216515500613

The Alexander polynomial as an intersection of two cycles in a symmetric power

Algebraic Topology 2015-10-27 v3

Authors: Nikita Kalinin

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Abstract

We consider a braid $\beta$ which acts on a punctured plane. Then we construct a local system on this plane and find a homology cicle $D$ in its symmetric power such that $D\cdot \beta(D)$ coincides with the Alexander polynomial of the plate closure of $\beta$ .

Keywords

alexander polynomial braid symmetric power local system homology cycle intersection theory plate closure

Cite

@article{arxiv.1311.2849,
  title  = {The Alexander polynomial as an intersection of two cycles in a symmetric power},
  author = {Nikita Kalinin},
  journal= {arXiv preprint arXiv:1311.2849},
  year   = {2015}
}

Comments

revision, the text is rearranged, details are added

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