Quantum extensions of ordinary maps
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- by Andre Kornell PDF
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Abstract:
We define a loop to be quantum nullhomotopic if and only if it admits a nonempty quantum set of extensions to the unit disk. We show that the canonical loop in the unit circle is not quantum nullhomotopic, but that every loop in the real projective plane is quantum nullhomotopic. Furthermore, we apply Kuiperâs theorem to show that the canonical loop admits a continuous family of extensions to the unit disk that is indexed by an infinite quantum space. We obtain these results using a purely topological condition that we show to be equivalent to the existence of a quantum family of extensions of a given map.References
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Additional Information
- Andre Kornell
- Affiliation: Department of Mathematics, University of California, Davis, Davis, California 95616
- MR Author ID: 1242738
- Email: kornell@math.ucdavis.edu
- Received by editor(s): December 30, 2018
- Published electronically: January 28, 2020
- Communicated by: Adrian Ioana
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 1971-1986
- MSC (2010): Primary 46L85; Secondary 54C20
- DOI: https://doi.org/10.1090/proc/14851
- MathSciNet review: 4078082