Lie structures in homotopy and isotopy calculi
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916717494534144 |
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| author | Kosanović, Danica |
| author_facet | Kosanović, Danica |
| contents | We establish compatibility of Lie structures that appear in homotopy calculus of functors and isotopy calculus of embeddings. On one hand, we give a new proof of the Johnson--Arone--Mahowald result describing the layers of the Goodwillie tower of the identity functor, and we directly compare the spectral Lie bracket with the classical Whitehead bracket on spaces. On the other hand, we geometrically define a bracket on the layers of the embedding calculus tower for embeddings of arcs. These results are unified through the same technical tool, a newly defined bracket on total homotopy fibres of collapsing cubes of wedge sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lie structures in homotopy and isotopy calculi Kosanović, Danica Algebraic Topology Geometric Topology 18F50, 57R40, 58D10 We establish compatibility of Lie structures that appear in homotopy calculus of functors and isotopy calculus of embeddings. On one hand, we give a new proof of the Johnson--Arone--Mahowald result describing the layers of the Goodwillie tower of the identity functor, and we directly compare the spectral Lie bracket with the classical Whitehead bracket on spaces. On the other hand, we geometrically define a bracket on the layers of the embedding calculus tower for embeddings of arcs. These results are unified through the same technical tool, a newly defined bracket on total homotopy fibres of collapsing cubes of wedge sums. |
| title | Lie structures in homotopy and isotopy calculi |
| topic | Algebraic Topology Geometric Topology 18F50, 57R40, 58D10 |
| url | https://arxiv.org/abs/2505.01375 |