Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups
Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups
Using integral methods we recover and generalize some results by F ́elix, Halperin and Thomas on the growth of the rational homology groups of free loop spaces, and obtain a new family of spaces whose p-torsion in homotopy groups grows exponentially and satisfies Moore’s Conjecture for all but finitely many primes. In view of the results, we conjecture that there should be a strong connection between exponential growth in the rational homotopy groups and the p-torsion homotopy groups for any prime p.
exponential growth, free loop space, homotopy exponent, Moore's Conjecture
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Huang, Ruizhi
86809c85-b4f2-4048-9894-c37cd234e12c
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Huang, Ruizhi
86809c85-b4f2-4048-9894-c37cd234e12c
Theriault, Stephen and Huang, Ruizhi
(2022)
Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups.
Annales de l'Institut Fourier.
(In Press)
Abstract
Using integral methods we recover and generalize some results by F ́elix, Halperin and Thomas on the growth of the rational homology groups of free loop spaces, and obtain a new family of spaces whose p-torsion in homotopy groups grows exponentially and satisfies Moore’s Conjecture for all but finitely many primes. In view of the results, we conjecture that there should be a strong connection between exponential growth in the rational homotopy groups and the p-torsion homotopy groups for any prime p.
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Accepted/In Press date: 17 November 2022
Keywords:
exponential growth, free loop space, homotopy exponent, Moore's Conjecture
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Local EPrints ID: 472862
URI: http://eprints.soton.ac.uk/id/eprint/472862
ISSN: 1777-5310
PURE UUID: 530b6004-ccc8-4eac-9a29-36ce37f3a15f
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Date deposited: 20 Dec 2022 17:42
Last modified: 17 Mar 2024 03:30
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Author:
Ruizhi Huang
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