Topological properties of caustics in five-dimensional spaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908493638795264 |
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| author | Sedykh, Vyacheslav D. |
| author_facet | Sedykh, Vyacheslav D. |
| contents | We give a list of universal linear relations between the Euler characteristics of manifolds consisting of multisingularities of a generic Lagrangian map into a five-dimensional space. From these relations it follows, in particular, that the numbers $D_5A_2, A_4A_3, A_4A_2^2$ of isolated self-intersection points of the corresponding types on any generic compact four-dimensional caustic are even. The numbers $D_4^+A_3+D_4^-A_3+E_6$, $D_4^+A_2^2+D_4^-A_2^2+\frac12A_4A_3$ are even as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09215 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological properties of caustics in five-dimensional spaces Sedykh, Vyacheslav D. Algebraic Geometry Symplectic Geometry 14P25, 14Q30, 53D12, 57R45, 58K15, 58K35 We give a list of universal linear relations between the Euler characteristics of manifolds consisting of multisingularities of a generic Lagrangian map into a five-dimensional space. From these relations it follows, in particular, that the numbers $D_5A_2, A_4A_3, A_4A_2^2$ of isolated self-intersection points of the corresponding types on any generic compact four-dimensional caustic are even. The numbers $D_4^+A_3+D_4^-A_3+E_6$, $D_4^+A_2^2+D_4^-A_2^2+\frac12A_4A_3$ are even as well. |
| title | Topological properties of caustics in five-dimensional spaces |
| topic | Algebraic Geometry Symplectic Geometry 14P25, 14Q30, 53D12, 57R45, 58K15, 58K35 |
| url | https://arxiv.org/abs/2401.09215 |