Lagrangian intersections and cuplength in generalised cohomology theories
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909184412352512 |
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| author | Hirschi, Amanda Porcelli, Noah |
| author_facet | Hirschi, Amanda Porcelli, Noah |
| contents | We find lower bounds on the number of intersection points between two relatively exact Hamiltonian isotopic Lagrangians. The bounds are given in terms of the cuplength of the Lagrangian in various multiplicative generalised cohomology theories. The intersection of the Lagrangians need not be transverse, however, we require certain orientation assumptions. This gives stronger bounds than previous estimates on the number of self-intersection points of a suitable closed, relatively exact Lagrangian diffeomorphic to Sp$(2)$ or Sp$(3)$. Our proof uses Lusternik-Schnirelmann theory, following and extending work by Hofer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_07559 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Lagrangian intersections and cuplength in generalised cohomology theories Hirschi, Amanda Porcelli, Noah Symplectic Geometry 53D12, 55N20 We find lower bounds on the number of intersection points between two relatively exact Hamiltonian isotopic Lagrangians. The bounds are given in terms of the cuplength of the Lagrangian in various multiplicative generalised cohomology theories. The intersection of the Lagrangians need not be transverse, however, we require certain orientation assumptions. This gives stronger bounds than previous estimates on the number of self-intersection points of a suitable closed, relatively exact Lagrangian diffeomorphic to Sp$(2)$ or Sp$(3)$. Our proof uses Lusternik-Schnirelmann theory, following and extending work by Hofer. |
| title | Lagrangian intersections and cuplength in generalised cohomology theories |
| topic | Symplectic Geometry 53D12, 55N20 |
| url | https://arxiv.org/abs/2211.07559 |