Mathematical Sciences: Dehn Surgery on Links

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8903599 Luecke The focus of this project is the study of different aspects of Dehn surgery on links in 3-manifolds. In particular, the investigator wants to sharpen a combinatorial analysis used in previous work to apply this analysis to the questions of when you can get the 3-sphere or reducible manifolds by Dehn surgery on a link and to the question of when a closed incompressible surface remains incompressible after Dehn surgery. He also wants to get a better understanding of a certain polygon in the Dehn surgery space of a knot that is related to the Dehn surgeries on the knot that have cyclic fundamental group.