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Low Dimensional Topology and Circle-valued Morse Functions

Offered By: IMSA via YouTube

Tags

Conference Talks Courses Knot Theory Courses Low-Dimensional Topology Courses Morse Theory Courses Circle-valued Morse Functions Courses Surface Diffeomorphisms Courses

Course Description

Overview

Explore a fascinating lecture on low-dimensional topology and circle-valued Morse functions presented by Alex Zupan from the University of Nebraska-Lincoln. Delve into an extension of the Casson-Gordon theorem, which originally applied to fibered knots in the 3-sphere. Learn how this result is expanded to non-fibered knots, introducing the concept of handle-ribbon knots. Discover the relationship between singular fibrations, determined by circular Morse functions, and the extension of knot exteriors over handlebodies. Gain insights into the conditions between ribbonness and sliceness in knot theory, and understand the significance of closed monodromy in this context. This hour-long talk, part of a conference at the University of Miami, presents joint work with Maggie Miller, offering a deep dive into advanced concepts in low-dimensional topology.

Syllabus

Conference: Low Dimensional Topology & Circle-valued Morse Functions, Alex Zupan


Taught by

IMSA

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