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Mathematische Annalen

, Volume 342, Issue 2, pp 255–271 | Cite as

Conjugations on 6-manifolds

  • Martin OlbermannEmail author
Article

Abstract

Conjugation spaces are spaces with an involution such that the fixed point set of the involution has \({\mathbb{Z} _2}\)-cohomology ring isomorphic to the \({\mathbb{Z} _2}\)-cohomology of the space itself, with the difference that all degrees are divided by two (e.g. \({\mathbb{C} {\rm P}^n}\) with the complex conjugation has \({\mathbb{R} {\rm P}^n}\) as fixed point set). One also requires that a certain conjugation equation is fulfilled. We give a new characterisation of conjugation spaces and apply it to the following realization problem: given M, a closed orientable 3-manifold, does there exist a simply connected 6-manifold X and a conjugation on X with fixed point set M? We give an affirmative answer.

Mathematics Subject Classification (2000)

57R91 55M35 55N91 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität BonnBonnGermany
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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