%0 Generic
%A Olbermann, Martin
%D 2007
%F heidok:7450
%K Simply-connected manifold , involution , cohomology , surgery , bordism
%R 10.11588/heidok.00007450
%T Conjugations on 6-Manifolds
%U https://archiv.ub.uni-heidelberg.de/volltextserver/7450/
%X Conjugation spaces are spaces with involution such that the fixed point set of the involution has Z/2-cohomology isomorphic to the Z/2-cohomology of the space itself, with the little difference that all degrees are divided by two (e.g. CP^n with the complex conjugation). One also requires that a certain conjugation equation is fulfilled. I give a new characterization of conjugation spaces and apply it to the following realization question: given M, a closed orientable 3-manifold, is there a 6-manifold X (with certain additional properties) containing M as submanifold such that M is the fixed point set of an orientation reversing involution on X? My main result is that for every such 3-manifold M there exists a simply connected conjugation 6-manifold X with fixed point set M.