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Composition of TG-Hyperbolic Virtual Knots

Description
"Thurston proved that the composition of any two classical knots is a satellite knot, and thus is not hyperbolic. In this thesis, we explore the composition of virtual knots, which are an extension of classical knots that generalize the idea of knots in the three sphere to knots in thickened surfaces. In particular, we prove that virtual knots behave much differently under composition: with only a few restrictions, the composition of two hyperbolic virtual knots is hyperbolic. We then prove strong lower bounds on the volume of the composition using information about the original knots. "

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Details
Title Composition of TG-Hyperbolic Virtual Knots
Author Simons, Alex
Advisor Adams, Colin Conrad
Department Mathematics
Type of Resource text
Date Issued 2021
Language eng
doi https://doi.org/10.36934/TR2021_155
filename 2021_Simons_Alex_Thesis_Final.pdf
Rights Contact Special Collections at [email protected]
Description "Thurston proved that the composition of any two classical knots is a satellite knot, and thus is not hyperbolic. In this thesis, we explore the composition of virtual knots, which are an extension of classical knots that generalize the idea of knots in the three sphere to knots in thickened surfaces. In particular, we prove that virtual knots behave much differently under composition: with only a few restrictions, the composition of two hyperbolic virtual knots is hyperbolic. We then prove strong lower bounds on the volume of the composition using information about the original knots. "
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ID Label Size Mimetype Created
OBJ OBJ datastream 27.16 MiB application/pdf 2021-05-28
TN TN 15.45 KiB image/png 2021-05-30