Presentation Title

The Role of Links in the Study of 3-Manifolds

Presenter Information

Anthony BosmanFollow

Presenter Status

Graduate Student, Mathematics

Presentation Type

Oral presentation: Blackboard chalk talk preferred (Can do Beamer slides if necessary.)

Session

B

Location

Chan Shun 108

Start Date

18-5-2017 4:20 PM

End Date

18-5-2017 4:40 PM

Presentation Abstract

3-manifolds are spaces that locally resemble Euclidean 3-dimensional space. The study and classification of such manifolds is of central concern in topology and geometry. We introduce the notion of surgery on a link as a means of obtaining 3-manifolds; a deep result of Lickorish and Wallace tells us that all sufficiently nice 3-manifolds can be obtained by such surgery. We then offer a new generalization of a well-known result on how a relationship between links gives information on how their associated zero surgery manifolds are related.

Biographical Sketch

Anthony is completing (recently competed) his doctorate in mathematics at Rice University. He is interested in low dimensional topology, in particular, the study of knots and links and how they relate to 3 and 4-manifolds. He will be joining the mathematics department at Andrews University as an assistant professor this year. Having lived all his life in sunny states, he is fearfully anticipating his first winter.

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May 18th, 4:20 PM May 18th, 4:40 PM

The Role of Links in the Study of 3-Manifolds

Chan Shun 108

3-manifolds are spaces that locally resemble Euclidean 3-dimensional space. The study and classification of such manifolds is of central concern in topology and geometry. We introduce the notion of surgery on a link as a means of obtaining 3-manifolds; a deep result of Lickorish and Wallace tells us that all sufficiently nice 3-manifolds can be obtained by such surgery. We then offer a new generalization of a well-known result on how a relationship between links gives information on how their associated zero surgery manifolds are related.