Flat surfaces and stability structures
We identify spaces of half-translation surfaces, equivalently complex curves with quadratic differential, with spaces of stability structures on Fukaya-type categories of punctured surfaces. This is achieved by new methods involving the complete classification of objects in these categories, which a...
| Main Authors: | , , |
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| Format: | Journal article |
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Springer
2017
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| _version_ | 1797103126017212416 |
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| author | Haiden, F Katzarkov, L Kontsevich, M |
| author_facet | Haiden, F Katzarkov, L Kontsevich, M |
| author_sort | Haiden, F |
| collection | OXFORD |
| description | We identify spaces of half-translation surfaces, equivalently complex curves with quadratic differential, with spaces of stability structures on Fukaya-type categories of punctured surfaces. This is achieved by new methods involving the complete classification of objects in these categories, which are defined in an elementary way. We also introduce a number of tools to deal with surfaces of infinite area, where structures similar to those in cluster algebra appear. |
| first_indexed | 2024-03-07T06:15:40Z |
| format | Journal article |
| id | oxford-uuid:f101615a-4b3f-446c-8c84-dfeac00792c2 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:15:40Z |
| publishDate | 2017 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:f101615a-4b3f-446c-8c84-dfeac00792c22022-03-27T11:52:29ZFlat surfaces and stability structuresJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f101615a-4b3f-446c-8c84-dfeac00792c2Symplectic Elements at OxfordSpringer2017Haiden, FKatzarkov, LKontsevich, MWe identify spaces of half-translation surfaces, equivalently complex curves with quadratic differential, with spaces of stability structures on Fukaya-type categories of punctured surfaces. This is achieved by new methods involving the complete classification of objects in these categories, which are defined in an elementary way. We also introduce a number of tools to deal with surfaces of infinite area, where structures similar to those in cluster algebra appear. |
| spellingShingle | Haiden, F Katzarkov, L Kontsevich, M Flat surfaces and stability structures |
| title | Flat surfaces and stability structures |
| title_full | Flat surfaces and stability structures |
| title_fullStr | Flat surfaces and stability structures |
| title_full_unstemmed | Flat surfaces and stability structures |
| title_short | Flat surfaces and stability structures |
| title_sort | flat surfaces and stability structures |
| work_keys_str_mv | AT haidenf flatsurfacesandstabilitystructures AT katzarkovl flatsurfacesandstabilitystructures AT kontsevichm flatsurfacesandstabilitystructures |