Realizing doubles: a conjugation zoo
| Autor: | Wolfgang Pitsch, Jérôme Scherer |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Ring (mathematics)
Pure mathematics Graded vector space Complex conjugate realization General Mathematics 010102 general mathematics Topological space Fixed point 01 natural sciences Cohomology 0103 physical sciences Euclidean geometry hopf invariant conjugation spaces 010307 mathematical physics Mathematics - Algebraic Topology 0101 mathematics Unit (ring theory) Mathematics |
| Popis: | Conjugation spaces are topological spaces equipped with an involution such that their fixed points have the same mod $2$ cohomology (as a graded vector space, a ring, and even an unstable algebra) but with all degrees divided by two, generalizing the classical examples of complex projective spaces under complex conjugation. Spaces which are constructed from unit balls in complex Euclidean spaces are called spherical and are very well understood. Our aim is twofold. We construct "exotic" conjugation spaces and study the realization question: which spaces can be realized as real loci, i.e., fixed points of conjugation spaces. We identify obstructions and provide examples of spaces and manifolds which cannot be realized as such. Comment: 16 pages |
| Databáze: | OpenAIRE |
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