TL;DR
This paper introduces a new concordance relation for links in the three-sphere based on Euler characteristic, forming a group structure that extends the knot concordance group with an infinitely generated complement.
Contribution
It defines a novel concordance group of links using Euler characteristic and explores variants with different surface orientations and embedding types.
Findings
The concordance group of links contains the knot concordance group as a direct summand.
The complement of the knot concordance group in the link concordance group is infinitely generated.
Variants include oriented, nonoriented, smooth, and locally flat embeddings.
Abstract
We define a notion of concordance based on Euler characteristic, and show that it gives rise to a concordance group of links in the three-sphere, which has the concordance group of knots as a direct summand with infinitely generated complement. We consider variants of this using oriented and nonoriented surfaces as well as smooth and locally flat embeddings.
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