On manifolds with corners
Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\infty)^k x R^{n-k}) have received comparatively little attention. The basic definitions in the subject are not agreed upon, there are several i...
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| Format: | Book section |
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International Press
2012
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| _version_ | 1797073953897840640 |
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| author | Joyce, D |
| author2 | Janeczko, S |
| author_facet | Janeczko, S Joyce, D |
| author_sort | Joyce, D |
| collection | OXFORD |
| description | Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\infty)^k x R^{n-k}) have received comparatively little attention. The basic definitions in the subject are not agreed upon, there are several inequivalent definitions in use of manifolds with corners, of boundary, and of smooth map, depending on the applications in mind. We present a theory of manifolds with corners which includes a new notion of smooth map f : X --> Y. Compared to other definitions, our theory has the advantage of giving a category Man^c of manifolds with corners which is particularly well behaved as a category: it has products and direct products, boundaries behave in a functorial way, and there are simple conditions for the existence of fibre products X x_Z Y in Man^c. Our theory is tailored to future applications in Symplectic Geometry, and is part of a project to describe the geometric structure on moduli spaces of J-holomorphic curves in a new way. But we have written it as a separate paper as we believe it is of independent interest. |
| first_indexed | 2024-03-06T23:29:17Z |
| format | Book section |
| id | oxford-uuid:6b739de4-8358-4895-a0cc-ff31237635a7 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:29:17Z |
| publishDate | 2012 |
| publisher | International Press |
| record_format | dspace |
| spelling | oxford-uuid:6b739de4-8358-4895-a0cc-ff31237635a72022-03-26T19:04:17ZOn manifolds with cornersBook sectionhttp://purl.org/coar/resource_type/c_3248uuid:6b739de4-8358-4895-a0cc-ff31237635a7Symplectic Elements at OxfordInternational Press2012Joyce, DJaneczko, SLi, JPhong, DManifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\infty)^k x R^{n-k}) have received comparatively little attention. The basic definitions in the subject are not agreed upon, there are several inequivalent definitions in use of manifolds with corners, of boundary, and of smooth map, depending on the applications in mind. We present a theory of manifolds with corners which includes a new notion of smooth map f : X --> Y. Compared to other definitions, our theory has the advantage of giving a category Man^c of manifolds with corners which is particularly well behaved as a category: it has products and direct products, boundaries behave in a functorial way, and there are simple conditions for the existence of fibre products X x_Z Y in Man^c. Our theory is tailored to future applications in Symplectic Geometry, and is part of a project to describe the geometric structure on moduli spaces of J-holomorphic curves in a new way. But we have written it as a separate paper as we believe it is of independent interest. |
| spellingShingle | Joyce, D On manifolds with corners |
| title | On manifolds with corners |
| title_full | On manifolds with corners |
| title_fullStr | On manifolds with corners |
| title_full_unstemmed | On manifolds with corners |
| title_short | On manifolds with corners |
| title_sort | on manifolds with corners |
| work_keys_str_mv | AT joyced onmanifoldswithcorners |