[Turkmath:4605] Fwd: BilTop - Talk (Oct 12)

[Cihan Okay]

Bilkent Topology Seminar on Oct 12:

---------- Forwarded message ---------
From: Cihan Okay <cihan.okay at bilkent.edu.tr>
Date: Wed, Oct 7, 2020 at 9:00 AM
Subject: BilTop - Talk (Oct 12)
To: Math Faculty <Mathfac at fen.bilkent.edu.tr>, <Mathgrad at fen.bilkent.edu.tr>,
<akiferdal at gmail.com>, <asli.ilhan at deu.edu.tr>, <bahra004 at umn.edu>, <
berrin at fen.bilkent.edu.tr>, <mgelvin at gmail.com>, <mpamuk at metu.edu.tr>, <
pasemra at metu.edu.tr>, Alex Degtyarev <degt at fen.bilkent.edu.tr>, Alihan <
alihan.serim at ug.bilkent.edu.tr>, Baran Zadeoğlu <baranzadeoglu at gmail.com>,
Betül Tolgay <tolgaybetul at gmail.com>, Claude Schochet <clsmath at gmail.com>,
Ergun Yalcin <yalcine at fen.bilkent.edu.tr>, Esat Akin <
esat.akin at ug.bilkent.edu.tr>, Esma Dirican <esmadirican131 at gmail.com>,
Laurence Barker <barker at fen.bilkent.edu.tr>, Melih Ucer <
melih.ucer at bilkent.edu.tr>, Mufit Sezer <sezer at fen.bilkent.edu.tr>, Oguz
Savk <oguz.savk at boun.edu.tr>, Ozgun Unlu <unluo at fen.bilkent.edu.tr>, Serdar
Baysal <serdar.baysal at bilkent.edu.tr>, Servin Bagheralmoosavi <
servin at bilkent.edu.tr>, Yara Ayman <yaraayman106 at gmail.com>, Zilan Akbas <
zilan.akbas at bilkent.edu.tr>
Cc: Gizem Ramanlı <gizem at fen.bilkent.edu.tr>


Dear all,

Here is the information for our next topology seminar:

Time: Oct 12, 2020 @ 13:40 UTC+3
Speaker:  Aslı Güçlukan
Affiliation: Dokuz Eylül University

Title: Small covers over a product of simplices

Abstract: Choi shows that there is a bijection between Davis–Januszkiewicz
equivalence classes of small covers over an $n$-cube and the set of acyclic
digraphs with $n$-labeled vertices. Using this, one can obtain a bijection
between weakly $(\mathbb{Z}/2)^n$-equivariant homeomorphism classes of
small covers over an $n$-cube and the isomorphism classes of acyclic
digraphs on labeled $n$ vertices up to local complementation and reordering
vertices.  To generalize these results to small covers over a product of
simplices we introduce the notion of $\omega$-weighted digraphs for a given
dimension function $\omega$. It turns out that there is a bijection between
Davis–Januszkiewicz equivalence classes of small covers over a product of
simplices and the set of acyclic $\omega$-weighted digraphs. After
introducing the notion of an $\omega$-equivalence, we also show that there
is a bijection between the weakly $(\mathbb{Z}/2)^n$-equivariant
homeomorphism classes of small covers over  $\Delta^{n_1}\times\cdots
\times \Delta^{n_k}$ and the set of $\omega$-equivalence classes of
$\omega$-weighted digraphs with $k$-labeled vertices $\{v_1, \cdots, v_k\}$
where $\omega$ is defined by $\omega(v_i)=n_i$ and $n=n_1+\cdots+n_k$. As
an example, we obtain a formula for the number of weakly
$(\mathbb{Z}/2)^n$-equivariant homeomorphism classes of small covers over
 a product of three simplices.

To see the upcoming talks visit: https://researchseminars.org/seminar/BilTop

I will send out the Zoom link on Monday.

Best,
Cihan
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