arXiv research

Surveying methods to create spaces with non-trivial self covers.

The paper proves conditions for self-covering manifolds to be fiber bundles over a circle.

Closed self-covering manifolds with abelian fundamental groups fiber over tori.

The paper studies knots in modular flows using self-covers.

Let $M$ be a closed manifold that admits a self-cover $p:M \to M$ of degree >1. We say p is strongly regular if all its iterates are regular covers. In this case, we establish an algebraic structure theorem for the fundamental group of $M$: We prove that $π_1(M)$ surjects onto a nontrivial free abelian group $A$, and t…

Counterexample disproves HK-conjecture for flat manifolds of dimension 9 and higher.

Generalized Thurston's characterization for branched coverings of the 2-sphere.

Extends Thurston's combinatorial characterization to all branched coverings of the 2-sphere.