The Knot Invariant $\Upsilon$ Using Grid Homologies

Viktória Földvári

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arXiv · 1903.05893

The Knot Invariant $\Upsilon$ Using Grid Homologies

Viktória Földvári

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Abstract

According to the idea of Ozsv\'ath, Stipsicz and Szab\'o, we define the knot invariant $\Upsilon$ without the holomorphic theory, using constructions from grid homology. We develop a homology theory using grid diagrams, and show that $\Upsilon$, as introduced this way, is a well-defined knot invariant. We reprove some important propositions using the new techniques, and show that $\Upsilon$ provides a lower bound on the unknotting number.

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Viktória Földvári. 2019-03-14. The Knot Invariant $\Upsilon$ Using Grid Homologies. https://arxiv.org/abs/1903.05893

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