Research ArticleNo Access

The knot invariant $Υ$ using grid homologies

Viktória Földvári

ELTE Eötvös Loránd University and Alfréd Rényi, Institute of Mathematics, Budapest, Hungary

https://doi.org/10.1142/S0218216521500516Cited by:1 (Source: Crossref)

Abstract

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

Keywords:

AMSC: 57K10, 57K14, 57K18

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