The L^2 signature of torus knots

We find a formula for the L2 signature of a (p,q) torus knot, which is the integral of the omega-signatures over the unit circle. We then apply this to a theorem of Cochran-Orr-Teichner to prove that the n-twisted doubles of the unknot, for n not 0 or 2, are not slice. This is a new proof of the result first proved by Casson and Gordon.Comment: 11 pages, Version 2 contains a note explaining that the main theorem of the paper has already been proved in earlier work by Kirby and Melvi

Open book decompositions for contact structures on Brieskorn manifolds

In this paper, we give an open book decomposition for the contact structures on some Brieskorn manifolds, in particular for the contact structures of Ustilovsky. The decomposition uses right-handed Dehn twists as conjectured by Giroux.Comment: 6 pages, no figure

Scissor equivalence for torus links

This article is about a natural distance function induced by smooth cobordisms between links. We show that the cobordism distance of torus links is determined by the profiles of their signature functions, up to a constant factor.Comment: 15 pages, 5 figures, Theorem 1 adde

Highly connected manifolds with positive Ricci curvature

We prove the existence of Sasakian metrics with positive Ricci curvature on certain highly connected odd dimensional manifolds. In particular, we show that manifolds homeomorphic to the 2k-fold connected sum of S^{2n-1} x S^{2n} admit Sasakian metrics with positive Ricci curvature for all k. Furthermore, a formula for computing the diffeomorphism types is given and tables are presented for dimensions 7 and 11.Comment: This is the version published by Geometry & Topology on 29 November 200