Bounds on the Crosscap Numbers of Torus Knots
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.
floor$ and $c(K) leq lfloor (n(K)+16)/12
floor$. The $(6n-2, 3)$ torus knots show that these bounds are sharp.
Speakers
Additional Information
Algebraic Topology Seminar 2007
Thomas Mattman (California State University, Chico)
Thomas Mattman (California State University, Chico)