Fujii, Michikazu Bordism theory with reality and duality theorem of Poincaré type. (English) Zbl 0702.57016 Math. J. Okayama Univ. 30, 151-160 (1988). The author studies the cobordism theory of closed differentiable manifolds with a given real structure on the stable tangent bundle. A \(\tau\)-manifold (M,t) is a \(C^{\infty}\)-manifold M together with a \(C^{\infty}\)-involution t: \(M\to M\), and a \(\tau\) map is an equivariant map between \(\tau\)-manifolds. A real structure on a \(\tau\)-vector bundle over a \(\tau\)-manifold (i.e. projection is a \(\tau\)-map) is a bundle isomorphism J with \(J^ 2=-id,\quad \tau J=(-J)\tau\) and \(proj(- J)=proj.\) The author proves a Poincaré duality theorem between the bordism and cobordism theory of manifolds with real structures. Reviewer: Y.F.Wong MSC: 57R90 Other types of cobordism 55N22 Bordism and cobordism theories and formal group laws in algebraic topology Keywords:manifold with involution; cobordism theory of closed differentiable manifolds with a given real structure on the stable tangent bundle PDFBibTeX XMLCite \textit{M. Fujii}, Math. J. Okayama Univ. 30, 151--160 (1988; Zbl 0702.57016)