Bounds on the Crosscap Numbers of Torus Knots

  • Date: 09/26/2007
Lecturer(s):

Thomas Mattman (California State University, Chico)

Location: 

University of British Columbia

Topic: 

In joint work with Sizemore, we build on Teragaito's calculation of the
crosscap number $c(K)$ of a torus knot $K$ to give bounds in terms of
the genus $g(K)$ and crossing number $n(K)$: $c(K) leq lfloor (g(K) +
9)/6
floor$ and $c(K) leq lfloor (n(K)+16)/12
floor$. The $(6n-2, 3)$ torus knots show that these bounds are sharp.

Other Information: 

Algebraic Topology Seminar 2007

Sponsor: 

pims