Topology Seminar (Main Talk): Rigidity for contact submanifolds in the higher dimension

Seminar | November 28 | 4:10-5 p.m. | 3 Evans Hall

 Roger Casals, UC Davis

 Department of Mathematics

In this talk, I will provide the first example of rigidity for contact submanifolds in higher dimensions. In three dimensions, there are examples of transverse knots in the 3-sphere which are isotopic as smooth knots, but not isotopic as transverse knots. These 3-dimensional examples were first provided by J. Birman and W. Menasco in 2006. The existence of such phenomenon in the higher-dimension has since remained an open question. I will explain how to construct, in any dimension, infinitely many pairs of smoothly isotopic contact submanifolds in the standard sphere which are not contact isotopic, thus resolving the question in the affirmative. This is based on joint work with J. Etnyre.