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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 .

Cyclic branched coverings of 2-bridge knots.

Alberto Cavicchioli, Beatrice Ruini, Fulvia Spaggiari (1999)

Revista Matemática Complutense

In this paper we study the connections between cyclic presentations of groups and the fundamental group of cyclic branched coverings of 2-bridge knots. Then we show that the topology of these manifolds (and knots) arises, in a natural way, from the algebraic properties of such presentations.

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