COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Differential Geometry and Topology Seminar > Infinite loop spaces and positive scalar curvature

## Infinite loop spaces and positive scalar curvatureAdd to your list(s) Download to your calendar using vCal - Oscar Randal-Williams, Cambridge
- Wednesday 16 October 2013, 16:00-17:00
- MR13.
If you have a question about this talk, please contact Ivan Smith. It is well known that there are topological obstructions to a manifold $M$ admitting a Riemannian metric of everywhere positive scalar curvature (psc): if $M$ is Spin and admits a psc metric, the Lichnerowiczâ€“WeitzenbĂ¶ck formula implies that the Dirac operator of $M$ is invertible, so the vanishing of the $\hat{A}$ genus is a necessary topological condition for such a manifold to admit a psc metric. If $M$ is simply-connected as well as Spin, then deep work of Gromov—Lawson, Schoen—Yau, and Stolz implies that the vanishing of (a small refinement of) the $\hat{A}$ genus is a sufficient condition for admitting a psc metric. For non-simply-connected manifolds, sufficient conditions for a manifold to admit a psc metric are not yet understood, and are a topic of much current research. I will discuss a related but somewhat different problem: if $M$ does admit a psc metric, what is the topology of the space $\mathcal{R}(M)$ of all psc metrics on it? Recent work of V. Chernysh and M. Walsh shows that this problem is unchanged when modifying $M$ by certain surgeries, and I will explain how this can be used along with work of Galatius and the speaker to show that the algebraic topology of $\mathcal{R}(M)$ for $M$ of dimension at least 6 is “as complicated as can possibly be detected by index-theory”. This is joint work with Boris Botvinnik and Johannes Ebert. This talk is part of the Differential Geometry and Topology Seminar series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- Differential Geometry and Topology Seminar
- Hanchen DaDaDash
- Interested Talks
- MR13
- School of Physical Sciences
- bld31
Note that ex-directory lists are not shown. |
## Other listsCambridge Language Sciences Early-Career Researchers Events FERSA Guest Lectures Cambridge/Africa Collaborative Research Programme Seminar Series Darwin Lectures and Seminars Global Food Futures Cambridge Migration Society## Other talksReplication or exploration? Sequential design for stochastic simulation experiments Bayesian optimal design for Gaussian process model Understanding model diversity in CMIP5 projections of westerly winds over the Southern Ocean How to Deploy Psychometrics Successfully in an Organisation Black and British Migration Alzheimer's talks 100 Problems around Scalar Curvature 'Ways of Reading, Looking, and Imagining: Contemporary Fiction and Its Optics' Constraint Analysis and Optimization in Medicine Development and Supply |