
TL;DR
This paper introduces a generalized Conway product for links, establishing a lower bound on the bridge number and demonstrating its tightness for an infinite class of links with high bridge numbers.
Contribution
It defines the generalized Conway product and proves a new lower bound on the bridge number, extending previous results.
Findings
Lower bound on bridge number: (K_{1} _{c} K_{2}) (K_{1}) - 1
The lower bound is tight for infinitely many links with high bridge numbers
Extends previous work on Conway products and bridge numbers
Abstract
Schubert proved that, given a composite link with summands and , the bridge number of satisfies the following equation: In ``Conway Produts and Links with Multiple Bridge Surfaces", Scharlemann and Tomova proved that, given links and , there is a Conway product such that In this paper, we define the generalized Conway product and prove the lower bound where is the distinguished factor of the generalized product. We go on to show this lower bound is tight for an infinite class of links with arbitrarily high bridge number.
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