Calorons, Nahm’s Equations on S 1 and Bundles over $${\mathbb{P}^{1} \times \mathbb{P}^{1}}$$

Connections on Principal S 1 – Bundles over Compacta ∗

Extremal Sasakian Metrics on S-bundles over S

In this note I prove the existence of extremal Sasakian metrics on S3-bundles over S2. These occur in a collection of open cones that I call a

A classification of S-bundles over S

We classify the total spaces of bundles over the four sphere with fiber a three sphere up to orientation preserving and reversing homotopy equivalence, homeomorphism and diffeomorphism. These total spaces have been of interest to both topologists and geometers. It has recently been shown by Grove and Ziller [GZ] that each of these total spaces admits metrics with nonnegative sectional curvature.

S-Bundles and Gerbes over Differentiable Stacks

We study S-bundles and S-gerbes over differentiable stacks in terms of Lie groupoids, and construct Chern classes and Dixmier-Douady classes in terms of analogues of connections and curvature. c © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS S-Fibrés et Gerbes sur des Champs Différentiables Résumé. On étudie les S-fibrés et les S-gerbes sur des champs différentiab...

The Heegaard Genus of Bundles over S

This is a largely expository paper exploring theorems of Rubinstein and Lackenby. Rubinstein’s Theorem studies the Heegaard genus of certain hyperbolic 3-manifolds that fiber over S and Lackenby’s Theorem studies the Heegaard genus of certain Haken manifolds. Our target audience are 3-manifold theorists with good understanding of Heegaard splittings but perhaps little experience with minimal su...