Closed manifold surgery obstructions and the Oozing Conjecture

TL;DR

This paper advances the understanding of surgery obstructions in closed oriented manifolds with finite fundamental groups, providing new examples that challenge the Oozing Conjecture from the 1980s.

Contribution

It completes the classification of surgery obstructions up to homotopy equivalence and introduces counterexamples to the Oozing Conjecture in higher codimensions.

Findings

New non-trivial obstructions for Arf invariant product formulas

Counterexamples to the Oozing Conjecture in codimensions ≥ 4

Complete description of surgery obstructions for certain manifolds

Abstract

We complete the description of surgery obstructions up to homotopy equivalence for closed oriented manifolds with finite fundamental group. New examples are presented of non-trivial obstructions for Arf invariant product formulas in codimensions $\geq 4$, which give counterexamples to the well-known ''Oozing Conjecture'' from the 1980's.