1. Self-covering, finiteness, and fibering over a circle.
- Author
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Qin, Lizhen, Su, Yang, and Wang, Botong
- Abstract
A topological space is called self-covering if it is a nontrivial cover of itself. We prove that a closed self-covering manifold M with free abelian fundamental group fibers over a circle under mild assumptions. In particular, we give a complete answer to the question whether a self-covering manifold with fundamental group \mathbb Z is a fiber bundle over S^1, except for the 4-dimensional smooth case. As an algebraic Hilfssatz, we develop a criterion for finite generation of modules over a commutative Noetherian ring. We also construct examples of self-covering manifolds with nonfree abelian fundamental group, which are not fiber bundles over S^1. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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