Hochschild Homology and Cohomology of Klein Surfaces
Within the framework of deformation quantization, a first step towards the study of star-products is the calculation of Hochschild cohomology. The aim of this article is precisely to determine the Hochschild homology and cohomology in two cases of algebraic varieties. On the one hand, we consider si...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2008 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2008
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149019 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Hochschild Homology and Cohomology of Klein Surfaces / F. Butin // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 18 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862713286051495936 |
|---|---|
| author | Butin, F. |
| author_facet | Butin, F. |
| citation_txt | Hochschild Homology and Cohomology of Klein Surfaces / F. Butin // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Within the framework of deformation quantization, a first step towards the study of star-products is the calculation of Hochschild cohomology. The aim of this article is precisely to determine the Hochschild homology and cohomology in two cases of algebraic varieties. On the one hand, we consider singular curves of the plane; here we recover, in a different way, a result proved by Fronsdal and make it more precise. On the other hand, we are interested in Klein surfaces. The use of a complex suggested by Kontsevich and the help of Groebner bases allow us to solve the problem.
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| first_indexed | 2025-12-07T17:43:30Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149019 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:43:30Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Butin, F. 2019-02-19T13:06:06Z 2019-02-19T13:06:06Z 2008 Hochschild Homology and Cohomology of Klein Surfaces / F. Butin // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 18 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 53D55; 13D03; 30F50; 13P10 https://nasplib.isofts.kiev.ua/handle/123456789/149019 Within the framework of deformation quantization, a first step towards the study of star-products is the calculation of Hochschild cohomology. The aim of this article is precisely to determine the Hochschild homology and cohomology in two cases of algebraic varieties. On the one hand, we consider singular curves of the plane; here we recover, in a different way, a result proved by Fronsdal and make it more precise. On the other hand, we are interested in Klein surfaces. The use of a complex suggested by Kontsevich and the help of Groebner bases allow us to solve the problem. This paper is a contribution to the Special Issue on Deformation Quantization. I would like to thank my thesis advisors Gadi Perets and Claude Roger for their ef ficient and likeable help, for their great availability, and for the time that they devoted to me all along this study. I also thank Daniel Sternheimer who paid attention to my work and the referees for their relevant remarks and their judicious advice. And I am grateful to Serge Parmentier for the rereading of my English text. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hochschild Homology and Cohomology of Klein Surfaces Article published earlier |
| spellingShingle | Hochschild Homology and Cohomology of Klein Surfaces Butin, F. |
| title | Hochschild Homology and Cohomology of Klein Surfaces |
| title_full | Hochschild Homology and Cohomology of Klein Surfaces |
| title_fullStr | Hochschild Homology and Cohomology of Klein Surfaces |
| title_full_unstemmed | Hochschild Homology and Cohomology of Klein Surfaces |
| title_short | Hochschild Homology and Cohomology of Klein Surfaces |
| title_sort | hochschild homology and cohomology of klein surfaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149019 |
| work_keys_str_mv | AT butinf hochschildhomologyandcohomologyofkleinsurfaces |