Room 515, Cosmology Building, National Taiwan University + Cisco WebEx, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館515研討室+ Cisco WebEx)
Classification of Neighbourhoods Around Leaves of a Singular Foliation
Simon-Raphaël Fischer (NCTS)
Abstract
This talk is about my recent work with Camille Laurent-Gengoux. I will present our results about classifying singular foliations admitting a given leaf
![](https://chart.googleapis.com/chart?cht=tx&chl=%24L%24&chf=bg,s,333333&chco=ffffff)
in a manifold
![](https://chart.googleapis.com/chart?cht=tx&chl=%24M%24&chf=bg,s,333333&chco=ffffff)
and a given transverse model
![](https://chart.googleapis.com/chart?cht=tx&chl=%24(%5Cmathbb%7BR%7D%5Ed%2C%20%5Ctau)%24&chf=bg,s,333333&chco=ffffff)
, where
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5Cmathbb%7BR%7D%5Ed%24&chf=bg,s,333333&chco=ffffff)
is the fibre of a normal bundle of
![](https://chart.googleapis.com/chart?cht=tx&chl=%24L%24&chf=bg,s,333333&chco=ffffff)
in
![](https://chart.googleapis.com/chart?cht=tx&chl=%24M%24&chf=bg,s,333333&chco=ffffff)
, and
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5Ctau%24&chf=bg,s,333333&chco=ffffff)
is a singular foliation in
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5Cmathbb%7BR%7D%5Ed%24&chf=bg,s,333333&chco=ffffff)
admitting 0 as a leaf. Such a classification is motivated by the fact that every foliation
![](https://chart.googleapis.com/chart?cht=tx&chl=%20%24%5Cmathcal%7BF%7D%24&chf=bg,s,333333&chco=ffffff)
induces a singular foliation in the fibres of a normal bundle, the
![](https://chart.googleapis.com/chart?cht=tx&chl=%7Btransverse%20(singular)%20foliation%7D&chf=bg,s,333333&chco=ffffff)
, and these transverse foliations at each point in
![](https://chart.googleapis.com/chart?cht=tx&chl=%24L%24&chf=bg,s,333333&chco=ffffff)
are canonically isomorphic. These isomorphisms are given by the parallel transport of what one calls
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5Cmathcal%7BF%7D%24&chf=bg,s,333333&chco=ffffff)
-connections.
The idea of this talk is to recover
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5Cmathcal%7BF%7D%24&chf=bg,s,333333&chco=ffffff)
given
![](https://chart.googleapis.com/chart?cht=tx&chl=%24(%5Cmathbb%7BR%7D%5Ed%2C%20%5Ctau)%24&chf=bg,s,333333&chco=ffffff)
, and we will see that in a local neighbourhood around
![](https://chart.googleapis.com/chart?cht=tx&chl=%24L%24%20&chf=bg,s,333333&chco=ffffff)
every foliation admitting
![](https://chart.googleapis.com/chart?cht=tx&chl=%24(%5Cmathbb%7BR%7D%5Ed%2C%20%5Ctau)%24&chf=bg,s,333333&chco=ffffff)
as transverse model is given by a certain infinite-dimensional principal bundle.
Meeting number (access code): 2514 282 6931
Meeting password: yyAn5reMW32
Organizers: Nicolau Sarquis Aiex (NTNU), Siao-Hao Guo (NTU), Chung-Jun Tsai (NTU)