Spaces of maps between real algebraic varieties
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913490342510592 |
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| author | Kucharz, Wojciech |
| author_facet | Kucharz, Wojciech |
| contents | Given two real algebraic varieties X and Y, we denote by R(X,Y) the set of all regular maps from X to Y. The set R(X,Y) is regarded as a topological subspace of the space C(X,Y) of all continuous maps from X to Y endowed with the compact-open topology. We prove, in a much more general setting than previously considered, that each path component of C(X,Y) contains at most one path component of R(X,Y), and for every positive integer k the inclusion map R(X,Y)-->C(X,Y) induces an isomorphism between the kth homotopy groups of the corresponding path components. We also identify several cases where this inclusion map is a weak homotopy equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13757 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spaces of maps between real algebraic varieties Kucharz, Wojciech Algebraic Geometry 14P05 (Primary) 54C35, 55P10 (Secondary) Given two real algebraic varieties X and Y, we denote by R(X,Y) the set of all regular maps from X to Y. The set R(X,Y) is regarded as a topological subspace of the space C(X,Y) of all continuous maps from X to Y endowed with the compact-open topology. We prove, in a much more general setting than previously considered, that each path component of C(X,Y) contains at most one path component of R(X,Y), and for every positive integer k the inclusion map R(X,Y)-->C(X,Y) induces an isomorphism between the kth homotopy groups of the corresponding path components. We also identify several cases where this inclusion map is a weak homotopy equivalence. |
| title | Spaces of maps between real algebraic varieties |
| topic | Algebraic Geometry 14P05 (Primary) 54C35, 55P10 (Secondary) |
| url | https://arxiv.org/abs/2408.13757 |