Grid diagrams and the Ozsvath-Szabo tau-invariant
Abstract
We use grid diagrams to investigate the Ozsvath-Szabo concordance invariant tau, and to prove that |tau(K1)-tau(K2)|<=g, whenever there is a genus g knot cobordism joining K1 to K2. This leads to an entirely grid diagram-based proof of Kronheimer-Mrowka's theorem, formerly known as the Milnor conjecture.
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