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．Seminars

	NCTS Differential Geometry Seminar

16:00 - 17:00, March 7, 2024 (Thursday)
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 $L$ in a manifold $M$ and a given transverse model $(\mathbb{R}^d, \tau)$ , where $\mathbb{R}^d$ is the fibre of a normal bundle of $L$ in $M$ , and $\tau$ is a singular foliation in $\mathbb{R}^d$ admitting 0 as a leaf. Such a classification is motivated by the fact that every foliation $\mathcal{F}$ induces a singular foliation in the fibres of a normal bundle, the ${transverse (singular) foliation}$ , and these transverse foliations at each point in $L$ are canonically isomorphic. These isomorphisms are given by the parallel transport of what one calls $\mathcal{F}$ -connections.

The idea of this talk is to recover $\mathcal{F}$ given $(\mathbb{R}^d, \tau)$ , and we will see that in a local neighbourhood around $L$ every foliation admitting $(\mathbb{R}^d, \tau)$ as transverse model is given by a certain infinite-dimensional principal bundle.

WebEX Link:https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=med5d1e02b13f14c91f2bda653fe1f186

Meeting number (access code): 2514 282 6931

Meeting password: yyAn5reMW32

Organizers: Nicolau Sarquis Aiex (NTNU), Siao-Hao Guo (NTU), Chung-Jun Tsai (NTU)