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Construction of Einstein metrics by generalized Dehn filling

Richard H. Bamler (2012)

Journal of the European Mathematical Society

In this paper, we present a new approach to the construction of Einstein metrics by a generalization of Thurston's Dehn filling. In particular in dimension 3, we will obtain an analytic proof of Thurston's result.

Contact topology and the structure of 5-manifolds with π 1 = 2

Hansjörg Geiges, Charles B. Thomas (1998)

Annales de l'institut Fourier

We prove a structure theorem for closed, orientable 5-manifolds M with fundamental group π 1 ( M ) = 2 and second Stiefel-Whitney class equal to zero on H 2 ( M ) . This structure theorem is then used to construct contact structures on such manifolds by applying contact surgery to fake projective spaces and certain 2 -quotients of  S 2 × S 3 .

Continuity of Barycentric Coordinates in Euclidean Topological Spaces

Karol Pąk (2011)

Formalized Mathematics

In this paper we present selected properties of barycentric coordinates in the Euclidean topological space. We prove the topological correspondence between a subset of an affine closed space of εn and the set of vectors created from barycentric coordinates of points of this subset.

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