Text only print
Full screen print
Tuesday Seminar on Topology
Seminar information archive ～03/21｜Next seminar｜Future seminars 03/22～
| 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)
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).
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).
