Mathematical Research Letters

Volume 18 (2011)

Number 6

Grid diagrams and the Ozsváth-Szabó tau-invariant

Pages: 1239 – 1257



Sucharit Sarkar (Department of Mathematics, Columbia University, New York, NY 10027, U.S.A.)


We use grid diagrams to investigate the \Ozsvath-\Szabo{} concordance invariant $\tau$, and to prove that $\left|\tau(K_1)-\tau(K_2)\right|\leq g$, whenever there is a genus $g$ knot cobordism joining $K_1$ to $K_2$. This leads to an entirely grid diagram-based proof of Kronheimer-Mrowka’s theorem, formerly known as the Milnor conjecture.

Published 20 February 2012