Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups
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| Format: | Preprint |
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2021
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| _version_ | 1866908340995489792 |
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| author | Huang, Ruizhi Theriault, Stephen |
| author_facet | Huang, Ruizhi Theriault, Stephen |
| contents | Using integral methods we recover and generalize some results by Félix, 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 $p$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2105_04426 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups Huang, Ruizhi Theriault, Stephen Algebraic Topology 55P35, 55P62 Using integral methods we recover and generalize some results by Félix, 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 $p$. |
| title | Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups |
| topic | Algebraic Topology 55P35, 55P62 |
| url | https://arxiv.org/abs/2105.04426 |