Branched cyclic covers and finite type invariants

Andrew Kricker

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arXiv · math/0003035

Branched cyclic covers and finite type invariants

Andrew Kricker

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Abstract

This work identifies a class of moves on knots which translate to $m$-equivalences of the associated $p$-fold branched cyclic covers, for a fixed $m$ and any $p$ (with respect to the Goussarov-Habiro filtration.) These moves are applied to give a flexible (if specialised) construction of knots for which the Casson-Walker-Lescop invariant (for example) of their $p$-fold branched cyclic covers may be readily calculated, for any choice of $p$. In the second part of this paper, these operations are illustrated by some theorems concerning the relationship of knot invariants obtained from finite type three-manifold invariants, via the branched cyclic covering construction, with the finite type theory of knots.

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BibTeX RIS

Andrew Kricker. 2000-07-08. Branched cyclic covers and finite type invariants. https://arxiv.org/abs/math/0003035

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