Concordance invariant Υ for balanced spatial graphs using grid homology

Abstract

The [Formula: see text] invariant is a concordance invariant using knot Floer homology. Földvári [The knot invariant [Formula: see text] using grid homologies,J. Knot Theory Ramifications 30(7) (2021) 2150051] gives a combinatorial restructure of it using grid homology. We extend the combinatorial [Formula: see text] invariant for balanced spatial graphs. Regarding links as spatial graphs, we give an upper and lower bound for the [Formula: see text] invariant when two links are connected by a cobordism. Also, we show that the combinatorial [Formula: see text] invariant is a concordance invariant for knots.