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 > Junior Geometry Seminar > The Fukaya-Morse algebra of a manifold

## The Fukaya-Morse algebra of a manifoldAdd to your list(s) Download to your calendar using vCal - Jack Smith (UCL)
- Friday 20 October 2017, 15:00-16:00
- MR13.
If you have a question about this talk, please contact Nils Prigge. Given a closed smooth manifold (and an appropriate Morse function and metric) you can define the Morse cochain complex, whose cohomology is isomorphic to that of the usual singular cochain complex. You can also define a product on the Morse complex, which induces the familiar cup product on cohomology, but in general it fails to be associative at chain level and does not encode all of the structure contained in the singular complex (e.g. Massey products). I will describe how an idea of Fukaya leads naturally to the notion of an A-infinity algebra, which is the correct weakening of the notion of associativity, and a way to build the structure of such an algebra on the Morse complex so that it captures (essentially) all of the information of the singular complex. If time permits I will also discuss how to quantise (i.e. deform) this algebra in certain ways. This talk is part of the Junior Geometry Seminar series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
## Other listsICE Summer Festival Persian Society talks CISA Panel on 2013 Italian Elections## Other talksNumerical solution of the radiative transfer equation with a posteriori error bounds Challenges to monetary policy in a global context CANCELLED-Open tools in Marchantia for plant bioengineering work and as a platform for elucidating morphogenesis CANCELLED DUE TO STRIKE ACTION Recent advances in understanding climate, glacier and river dynamics in high mountain Asia The interpretation of black hole solutions in general relativity Grammar Variational Autoencoder |