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Linking numbers of pseudo-branch curves

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Speaker: 
Alexandra Kjuchukova
Affiliation: 
University of Wisconsin-Madison
Date: 
Fri, 21/10/2016 - 13:30 - 14:30
Location: 
MPIM Lecture Hall

Let $K$ be a knot in $S^3$ and $f\colon M \to S^3$ a cover branched along $K$. Under certain hypotheses, the linking numbers in $M$ between the components of $f^{-1}(K)$ are an invariant of $K$. This invariant was crucial for expanding the knot table to include knots of more than 8 crossings, among other uses. Also important but less well-studied are linking numbers between ``pseudo-branch curves", or lifts to $M$ of simple closed curves in the complement of $K$. I describe a method for computing such linking numbers. I will also explain the motivation for this work, and how it can be used in the classification of branched covers between four-manifolds with singular branching sets. Joint with Patricia Cahn.
 

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