### Equivalences to the triangulation conjecture.

Randall, Duane (2002)

Algebraic & Geometric Topology

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Randall, Duane (2002)

Algebraic & Geometric Topology

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Nicholaas H. Kuiper (1967)

Publications Mathématiques de l'IHÉS

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Samelson, Hans (1951)

Portugaliae mathematica

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Im, Young Ho, Kang, Mee Kwang, Woo, Ki Mun (1998)

International Journal of Mathematics and Mathematical Sciences

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Juraj Lörinc (2003)

Mathematica Slovaca

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Hansjörg Geiges, Charles B. Thomas (1998)

Annales de l'institut Fourier

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We prove a structure theorem for closed, orientable 5-manifolds $M$ with fundamental group ${\pi}_{1}\left(M\right)={\mathbb{Z}}_{2}$ and second Stiefel-Whitney class equal to zero on ${H}_{2}\left(M\right)$. This structure theorem is then used to construct contact structures on such manifolds by applying contact surgery to fake projective spaces and certain ${\mathbb{Z}}_{2}$-quotients of ${S}^{2}\times {S}^{3}$.

Kreck, Matthias (1999)

Annals of Mathematics. Second Series

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S. Buoncristiano, M. Dedò (1980)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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