The Role of Links in the Study of 3-Manifolds
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.
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.