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SUMMARY:Aslı Güçlükan (Dokuz Eylul University)
DTSTART:20201012T104000Z
DTEND:20201012T113000Z
DTSTAMP:20260422T135419Z
UID:BilTop/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BilTop/7/">S
 mall covers over a product of simplices</a>\nby Aslı Güçlükan (Dokuz E
 ylul University) as part of Bilkent Topology Seminar\n\nLecture held in SB
 -Z11.\n\nAbstract\nChoi shows that there is a bijection between Davis–Ja
 nuszkiewicz equivalence classes of small covers over an $n$-cube and the s
 et of acyclic digraphs with $n$-labeled vertices. Using this\, one can obt
 ain a bijection between weakly $(\\mathbb{Z}/2)^n$-equivariant homeomorphi
 sm 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 p
 roduct of simplices we introduce the notion of $\\omega$-weighted digraphs
  for a given dimension function $\\omega$. It turns out that there is a bi
 jection between Davis–Januszkiewicz equivalence classes of small covers 
 over a product of simplices and the set of acyclic $\\omega$-weighted digr
 aphs. After introducing the notion of an $\\omega$-equivalence\, we also s
 how that there is a bijection between the weakly $(\\mathbb{Z}/2)^n$-equiv
 ariant 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 $n=n_1+\\c
 dots+n_k$. 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.\n
LOCATION:https://researchseminars.org/talk/BilTop/7/
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