On the quotient of the homology cobordism group by Seifert spaces

TL;DR

This paper proves that when you divide the integer homology cobordism group by the subgroup generated by Seifert fibered spaces, the resulting quotient is infinitely large, revealing complex underlying structure.

Contribution

It establishes that the quotient of the homology cobordism group by Seifert spaces is infinitely generated, a new insight into the group's structure.

Findings

The quotient group is infinitely generated.

Seifert fibered spaces generate a proper subgroup.

The structure of the homology cobordism group is highly complex.

Abstract

We prove that the quotient of the integer homology cobordism group by the subgroup generated by the Seifert fibered spaces is infinitely generated.