Self-mapping Degrees of 3-Manifolds

TL;DR

This paper characterizes the set of possible degrees of self-maps for each closed oriented 3-manifold within Thurston's classification, providing a comprehensive understanding of self-mapping degrees in 3-dimensional topology.

Contribution

It explicitly determines the degrees of self-maps for all closed oriented 3-manifolds in Thurston's framework, a complete classification not previously established.

Findings

Set of degrees for each 3-manifold explicitly given

Unified description across Thurston's geometrization types

Advances understanding of self-mapping properties in 3D topology

Abstract

For each closed oriented 3-manifold $M$ in Thurston's picture, the set of degrees of self-maps on $M$ is given.