Concordance invariant ${\rm Y}$ for balanced spatial graphs using grid homology

Abstract

The ${\rm Y}$ invariant is a concordance invariant defined by using knot Floer homology. Földvári gives a combinatorial restructure of it using grid homology. We extend the combinatorial ${\rm Y}$ 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 ${\rm Y}$ when two links are connected by a cobordism. Also we show that the combinatorial ${\rm Y}$ is a concordance invariant for knots.

27 pages, 18 figures; typos corrected, proofread