Floyd’s manifold is a conjugation space

• Autores: Wolfgang Pitsch , Jérôme Scherer
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 24, Nº 3, 2023, págs. 1487-1497
• Idioma: inglés
• DOI: 10.2422/2036-2145.202106_002
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• Resumen

  • E. E. Floyd showed in 1973 that there exist only two nontrivial cobor- dism classes that contain manifolds with three cells, and that they lie in dimen- sions 10 and 5. We prove that there is an action of the cyclic group C2 on the 10-dimensional Floyd manifold which turns it into a conjugation manifold in the sense of Hausmann, Holm, and Puppe. The submanifold of fixed points is the 5-dimensional Floyd manifold, whose cohomology is isomorphic to that of the large one, scaled down by dividing the cohomological degree by a factor two.