A generalization of Montgomery-Yang correspondence

TL;DR

This paper generalizes the Montgomery-Yang correspondence to relate diffeomorphism classes of spin d-twisted homology P^3 to isotopy classes of embeddings of S^3 into S^6, and uses this to prove the existence of free involutions.

Contribution

It introduces a generalized correspondence between specific 3-manifold classes and embeddings, extending Montgomery-Yang's original work.

Findings

Established a one-to-one correspondence between the classes.

Proved the existence of free involutions on these manifolds.

Extended the application of the original correspondence.

Abstract

In this paper, we want to construct a one-to-one correspondence from the set of diffeomorphism classes of spin $d$-twisted homology $\mc P^3$ to the set of isotopy classes of the embedding from $S^3$ to $S^6$, which is a generalization of the Montgomery-Yang correspondence. Furthermore, we will apply this generalized correspondence to prove the existence of free involution on these $d$-twisted homology $\mc P^3$.