Selective Categories and Linear Canonical Relations
A construction of Wehrheim and Woodward circumvents the problem that compositions of smooth canonical relations are not always smooth, building a category suitable for functorial quantization. To apply their construction to more examples, we introduce a notion of highly selective category, in which...
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| Дата: | 2014 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146541 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Selective Categories and Linear Canonical Relations / D. Li-Bland, A. Weinstein // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 23 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1465412019-02-10T01:25:08Z Selective Categories and Linear Canonical Relations Li-Bland, D. Weinstein, A. A construction of Wehrheim and Woodward circumvents the problem that compositions of smooth canonical relations are not always smooth, building a category suitable for functorial quantization. To apply their construction to more examples, we introduce a notion of highly selective category, in which only certain morphisms and certain pairs of these morphisms are ''good''. We then apply this notion to the category SLREL of linear canonical relations and the result WW(SLREL) of our version of the WW construction, identifying the morphisms in the latter with pairs (L,k) consisting of a linear canonical relation and a nonnegative integer. We put a topology on this category of indexed linear canonical relations for which composition is continuous, unlike the composition in SLREL itself. Subsequent papers will consider this category from the viewpoint of derived geometry and will concern quantum counterparts. 2014 Article Selective Categories and Linear Canonical Relations / D. Li-Bland, A. Weinstein // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 23 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D50; 18F99; 81S10 DOI:10.3842/SIGMA.2014.100 http://dspace.nbuv.gov.ua/handle/123456789/146541 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
A construction of Wehrheim and Woodward circumvents the problem that compositions of smooth canonical relations are not always smooth, building a category suitable for functorial quantization. To apply their construction to more examples, we introduce a notion of highly selective category, in which only certain morphisms and certain pairs of these morphisms are ''good''. We then apply this notion to the category SLREL of linear canonical relations and the result WW(SLREL) of our version of the WW construction, identifying the morphisms in the latter with pairs (L,k) consisting of a linear canonical relation and a nonnegative integer. We put a topology on this category of indexed linear canonical relations for which composition is continuous, unlike the composition in SLREL itself. Subsequent papers will consider this category from the viewpoint of derived geometry and will concern quantum counterparts. |
| format |
Article |
| author |
Li-Bland, D. Weinstein, A. |
| spellingShingle |
Li-Bland, D. Weinstein, A. Selective Categories and Linear Canonical Relations Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Li-Bland, D. Weinstein, A. |
| author_sort |
Li-Bland, D. |
| title |
Selective Categories and Linear Canonical Relations |
| title_short |
Selective Categories and Linear Canonical Relations |
| title_full |
Selective Categories and Linear Canonical Relations |
| title_fullStr |
Selective Categories and Linear Canonical Relations |
| title_full_unstemmed |
Selective Categories and Linear Canonical Relations |
| title_sort |
selective categories and linear canonical relations |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146541 |
| citation_txt |
Selective Categories and Linear Canonical Relations / D. Li-Bland, A. Weinstein // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 23 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT liblandd selectivecategoriesandlinearcanonicalrelations AT weinsteina selectivecategoriesandlinearcanonicalrelations |
| first_indexed |
2023-05-20T17:25:02Z |
| last_indexed |
2023-05-20T17:25:02Z |
| _version_ |
1796153239921491968 |