Realizing doubles: A conjugation zoo

Wolfgang Pitsch*, Jérôme Scherer

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review


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.

Original languageAmerican English
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Publication statusAccepted in press - 2020


  • Conjugation spaces
  • Hopf invariant
  • realization


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