Topology Atlas | Conferences

Knots in the Triangle (Knots kNot in Washington)
April 29 - May 1, 2016
North Carolina State University
Raleigh NC, USA

Organizers
Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

Conference Homepage


Exceptional Cosmetic Surgeries on S3.
by
Huygens Ravelomanana
University of Georgia

Two distinct Dehn surgeries on the same knot are called cosmetic if they produces homeomorphic 3-manifolds. The knot cosmetic surgery problem asks if cosmetic surgeries do exist. One of my result is that the slope of an exceptional truly cosmetic surgery (if it exists) on a hyperbolic knot in S3 must be ±1 and the surgery must be irreducible and toroidal but not Seifert fibred. This restricts the type of knots which can admit exceptional truly cosmetic surgeries. In particular there are no exceptional truly cosmetic surgeries on alternating hyperbolic knots in S3. There are no exceptional truly cosmetic surgeries on arborescent knots in S3.

Date received: February 17, 2016

Copyright © 2016 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbmk-05.