Tuesday Seminar on Topology

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Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.)
Organizer(s) KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya

2016/02/16

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Luc Menichi (University of Angers)
String Topology, Euler Class and TNCZ free loop fibrations (ENGLISH)
[ Abstract ]
Let $M$ be a connected, closed oriented manifold.
Chas and Sullivan have defined a loop product and a loop coproduct on
$H_*(LM;¥mathbb{F})$, the homology of the
free loops on $M$ with coefficients in the field $¥mathbb{F}$.
By studying this loop coproduct, I will show that if the free loop
fibration
$¥Omega M¥buildrel{i}¥over¥hookrightarrow
LM¥buildrel{ev}¥over¥twoheadrightarrow M$
is homologically trivial, i.e. $i^*:H^*(LM;¥mathbb{F})¥twoheadrightarrow
H^*(¥Omega M;¥mathbb{F})$ is onto,
then the Euler characteristic of $M$ is divisible by the characteristic
of the field $¥mathbb{F}$
(or $M$ is a point).