On the bialgebra structure of the free loop homology
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914457361317888 |
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| author | Saneblidze, Samson |
| author_facet | Saneblidze, Samson |
| contents | We introduce a commutative product of degree $-n$ on the homology $H_\ast(X)$ of an $n$-dimensional special cubical set $X$ and lift it on the free loop homology $H_\ast(ΛM)$ for $M=|X|$ to be the geometric realization. These products agree with the intersection and string topology products respectively when $M$ is an oriented closed manifold, and we
establish the compatibility relation between the string topology
product and the standard coproduct on $H_\ast(ΛM).$ Motivated by the above relationship we introduce the notion of loop bialgebra for differential graded coalgebras $C$ by means of the coHochschild complex $ΛC.$ We calculate the loop bialgebra structure for some spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06698 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the bialgebra structure of the free loop homology Saneblidze, Samson Algebraic Topology 55P35, 55U05, 52B05, 18F20 We introduce a commutative product of degree $-n$ on the homology $H_\ast(X)$ of an $n$-dimensional special cubical set $X$ and lift it on the free loop homology $H_\ast(ΛM)$ for $M=|X|$ to be the geometric realization. These products agree with the intersection and string topology products respectively when $M$ is an oriented closed manifold, and we establish the compatibility relation between the string topology product and the standard coproduct on $H_\ast(ΛM).$ Motivated by the above relationship we introduce the notion of loop bialgebra for differential graded coalgebras $C$ by means of the coHochschild complex $ΛC.$ We calculate the loop bialgebra structure for some spaces. |
| title | On the bialgebra structure of the free loop homology |
| topic | Algebraic Topology 55P35, 55U05, 52B05, 18F20 |
| url | https://arxiv.org/abs/2604.06698 |