Grid diagrams and the Ozsvath-Szabo tau-invariant

Sucharit Sarkar

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arXiv · 1011.5265

Grid diagrams and the Ozsvath-Szabo tau-invariant

Sucharit Sarkar

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Abstract

We use grid diagrams to investigate the Ozsvath-Szabo concordance invariant tau, and to prove that |tau(K_1)-tau(K_2)|<=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.

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Sucharit Sarkar. 2012-11-22. Grid diagrams and the Ozsvath-Szabo tau-invariant. https://arxiv.org/abs/1011.5265

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