Session S23 - Group actions in Differential Geometry

Friday, July 23, 16:40 ~ 17:10 UTC-3

Low-dimensional double disk bundles

Fernando Galaz-García

Durham University, United Kingdom   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Manifolds that admit a double disk bundle decomposition have played an important role in the study of closed Riemannian manifolds with positive or nonnegative (sectional) curvature. In particular, the presence of such a decomposition has proven useful both in producing new examples and in proving classification results under additional symmetry assumptions. More generally, Grove's Double Soul Conjecture asserts that any closed simply connected manifold of nonnegative curvature is the union of two disk bundles, while the Bott Conjecture asserts that any closed simply connected nonnegative must be rationally elliptic. In this talk I will discuss different sources of examples as well as classification results for (rationally elliptic) double disk bundles in low dimensions.

Joint work with Jason DeVito (University of Tennessee at Martin, USA) and Martin Kerin (National University of Ireland Galway, Ireland).

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