[Turkmath:542] Bahar Acu at MSGSU, Tuesday, June 2, 14:30

[Mohan Ravichandran]

Dear All,

 Bahar Acu from USC will talk this Tuesday at the Mimar Sinan Bomonti
campus.

*Title*: Higher Dimensional Symplectic Mapping Class Group Relations
Generalizing the Chain Relation

*Abstract:* In the first part of the talk, we will introduce basics
and related notions of contact
and symplectic geometry, i.e., vocabulary needed for the second part
of the talk. It is planned
 to be accesible to all graduate students.\

      In the second part: we will examine symplectomorphisms of higher
dimensional symplectic
manifolds by using fibered Dehn twists first introduced by Biran and
Giroux.  The Weinstein
domain of interest in this talk is  $W^{2n}=\{f(z_0, \dots,
z_n)=\delta\} \cap B^{2n+2}$,
given by a homogeneous polynomial $f$, which has a Boothby-Wang type boundary.
Despite the fact that many fibered Dehn twists cannot be expressed as
a product of Dehn
twists, we are still able to show that $\partial W$ has an open book
decomposition carrying
 a fibered Dehn twist which is symplectically isotopic to a product of
$k(k -1)^n$
 right-handed Dehn twists along Lagrangian spheres. Moreover, we show that this
identification yields a generalization of the classical chain relation
on surfaces. This is
joint work with Russell Avdek.

First Talk : 14:30

Second Talk : 15:45

Place : 106, Bomonti campus, MSGSU

Date : June 2, Tuesday

Best,

Mohan
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