Surveying methods to create spaces with non-trivial self covers.
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8 results for “self-covers”
problem Creating spaces with non-trivial self covers.
method Surveying techniques for constructing spaces, including low and high dimension continua.
result Discussion of open problems related to self covering phenomena.
The paper proves conditions for self-covering manifolds to be fiber bundles over a circle.
problem Conditions for self-covering manifolds to be fiber bundles over a circle.
method Developed a criterion for finite generation of modules over a commutative Noetherian ring and proved conditions for fiber bundles.
result Proved that certain self-covering manifolds with free abelian fundamental group are fiber bundles over a circle.
Closed self-covering manifolds with abelian fundamental groups fiber over tori.
problem Understanding the structure of self-covering manifolds with abelian fundamental groups.
method Proving the existence of fiberings over tori under mild assumptions.
result Closed self-covering manifolds with abelian fundamental groups fiber over tori in various senses.
The paper studies self-covers of manifolds and their algebraic structures.
problem Understanding the algebraic structure of manifolds with self-covers.
method Analyzes self-covers of manifolds and their induced linear endomorphisms.
result Establishes an algebraic structure theorem for the fundamental group of manifolds.
The paper studies knots in modular flows using self-covers.
problem Understanding topological properties of modular knots.
method Constructing templates for Anosov flows and studying closed geodesics.
result Explicit construction of an infinite family of links with the trefoil.
Counterexample disproves HK-conjecture for flat manifolds of dimension 9 and higher.
problem Disproving the HK-conjecture for flat manifolds of various dimensions.
method Using flat manifolds of dimension 9 and higher, constructing counterexamples.
result Minimal dimension 9 is required for counterexamples, and higher dimensions are possible.
Generalized Thurston's characterization for branched coverings of the 2-sphere.
problem Characterize branched coverings of the 2-sphere.
method Introduced local balance and operations against balanced graphs.
result New proof of a theorem by Eremenko-Gabrielov-Mukhin-Tarasov-Varchenko.
Extends Thurston's combinatorial characterization to all branched coverings of the 2-sphere.
problem Characterizing branched coverings of the 2-sphere.
method Generalizing Thurston's local balancing to all branched coverings.
result Provides a new proof for a theorem concerning real rational functions.