Concordance invariant $\Upsilon$ for balanced spatial graphs using grid homology

Hajime Kubota

doi:10.1142/s0218216523500888

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arXiv · 2206.15048

Concordance invariant $\Upsilon$ for balanced spatial graphs using grid homology

Hajime Kubota

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Abstract

The $\Upsilon$ invariant is a concordance invariant defined by using knot Floer homology. F\"{o}ldv\'{a}ri gives a combinatorial restructure of it using grid homology. We extend the combinatorial $\Upsilon$ invariant for balanced spatial graph using grid homology for balanced spatial graph. Regarding links as spatial graphs, we give a upper and lower bounds for $\Upsilon$ when two links are connected by a cobordism. Also we show that the combinatorial $\Upsilon$ is a concordance invariant for knots.

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Hajime Kubota. 2022-06-30. Concordance invariant $\Upsilon$ for balanced spatial graphs using grid homology. https://doi.org/10.1142/s0218216523500888

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