On the complement to a real caustic germ of type $E_6$
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909651979730944 |
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| author | Sedykh, Vyacheslav D. |
| author_facet | Sedykh, Vyacheslav D. |
| contents | We prove that the complement to the caustic of a stable Lagrangian map germ of type $E_6^\pm$ has seven connected components, six of which are contractible and one is homotopy equivalent to a circle. The inverse image of the noncontractible component under this map has three connected components. The restriction of the map to one of them is a two-sheeted covering; the restriction to each of the other two is a diffeomorphism. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_15748 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the complement to a real caustic germ of type $E_6$ Sedykh, Vyacheslav D. Algebraic Geometry 14P25, 58K15 (Primary) 14Q30, 53D12, 57R45, 58K35, 58K60 (Secondary) We prove that the complement to the caustic of a stable Lagrangian map germ of type $E_6^\pm$ has seven connected components, six of which are contractible and one is homotopy equivalent to a circle. The inverse image of the noncontractible component under this map has three connected components. The restriction of the map to one of them is a two-sheeted covering; the restriction to each of the other two is a diffeomorphism. |
| title | On the complement to a real caustic germ of type $E_6$ |
| topic | Algebraic Geometry 14P25, 58K15 (Primary) 14Q30, 53D12, 57R45, 58K35, 58K60 (Secondary) |
| url | https://arxiv.org/abs/2310.15748 |