Framings of $W_{g,1}$

TL;DR

This paper classifies the different ways to assign framings to the manifold $W_{g,1}$, which is a connected sum of a disk with multiple copies of $S^n imes S^n$, up to homotopy and diffeomorphism.

Contribution

It provides a complete computation of the set of framings of $W_{g,1}$ relative to the boundary, up to homotopy and diffeomorphism.

Findings

Explicit classification of framings for $W_{g,1}$.

Results applicable to high-dimensional manifold topology.

Advances understanding of boundary-relative framings.

Abstract

We compute the set of framings of $W_{g,1} = D^{2n} \# (S^n \times S^n)^{\# g}$, up to homotopy and diffeomorphism relative to the boundary.