Obstruction sequences to homotopy equivalences
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909799708360704 |
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| author | Emprin, Coline |
| author_facet | Emprin, Coline |
| contents | We develop an obstruction theory for the existence of gauge equivalences in complete differential graded Lie algebras. Specifically, this theory provides a characterization of homotopy equivalences between differential graded algebras governed by operads or properads, potentially colored in a groupoid. We apply this framework to establish new homotopy equivalence results in both algebraic topology and algebraic geometry, with a particular focus on the study of minimal models for highly connected varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17895 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Obstruction sequences to homotopy equivalences Emprin, Coline Algebraic Topology Algebraic Geometry Quantum Algebra 18D50, 18G55, 17B60 16W25, 13D10 We develop an obstruction theory for the existence of gauge equivalences in complete differential graded Lie algebras. Specifically, this theory provides a characterization of homotopy equivalences between differential graded algebras governed by operads or properads, potentially colored in a groupoid. We apply this framework to establish new homotopy equivalence results in both algebraic topology and algebraic geometry, with a particular focus on the study of minimal models for highly connected varieties. |
| title | Obstruction sequences to homotopy equivalences |
| topic | Algebraic Topology Algebraic Geometry Quantum Algebra 18D50, 18G55, 17B60 16W25, 13D10 |
| url | https://arxiv.org/abs/2509.17895 |