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

Nikita Kalinin^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a braid β which acts on a punctured plane. Then we construct a local system on this plane and find a homology cycle D in its symmetric power, such that D β(D) coincides with the Alexander polynomial of the plait closure of β.

Original language	English
Article number	1550061
Journal	Journal of Knot Theory and its Ramifications
Volume	24
Issue number	12
DOIs	https://doi.org/10.1142/S0218216515500613
State	Published - 1 Oct 2015
Externally published	Yes

Keywords

Braid group action
the Alexander polynomial

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10.1142/S0218216515500613

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title = "The Alexander polynomial as an intersection of two cycles in a symmetric power",

abstract = "We consider a braid β which acts on a punctured plane. Then we construct a local system on this plane and find a homology cycle D in its symmetric power, such that D β(D) coincides with the Alexander polynomial of the plait closure of β.",

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AB - We consider a braid β which acts on a punctured plane. Then we construct a local system on this plane and find a homology cycle D in its symmetric power, such that D β(D) coincides with the Alexander polynomial of the plait closure of β.

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KW - the Alexander polynomial

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

Abstract

Keywords

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