The Morse complex is an $\infty$-functor
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914449556766720 |
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| author | Cazassus, Guillem |
| author_facet | Cazassus, Guillem |
| contents | We show that the Morse complex of a compact Lie monoid can be given the structure of an $f$-bialgebra, a chain-level version of bialgebras introduced in [CHM24]; and that this assignment defines an $\infty$-functor. As a consequence, we obtain two other $\infty$-functors mapping closed smooth manifolds to their Morse complexes with their $A_\infty$-coalgebra structures; and closed smooth manifolds with compact Lie group actions to their Morse complexes, with a ``$u$-bimodule'' structure (a bimodule version for $f$-bialgebras). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01362 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Morse complex is an $\infty$-functor Cazassus, Guillem Algebraic Topology Category Theory Geometric Topology Symplectic Geometry We show that the Morse complex of a compact Lie monoid can be given the structure of an $f$-bialgebra, a chain-level version of bialgebras introduced in [CHM24]; and that this assignment defines an $\infty$-functor. As a consequence, we obtain two other $\infty$-functors mapping closed smooth manifolds to their Morse complexes with their $A_\infty$-coalgebra structures; and closed smooth manifolds with compact Lie group actions to their Morse complexes, with a ``$u$-bimodule'' structure (a bimodule version for $f$-bialgebras). |
| title | The Morse complex is an $\infty$-functor |
| topic | Algebraic Topology Category Theory Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2505.01362 |