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SUMMARY:Manisha Binjola (IIT Delhi)
DTSTART:20201118T053000Z
DTEND:20201118T063000Z
DTSTAMP:20260423T021418Z
UID:CATGT/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CATGT/19/">O
 n regular genus of PL 4-manifold with boundary</a>\nby Manisha Binjola (II
 T Delhi) as part of Applications of Combinatorics in Algebra\, Topology an
 d Graph Theory\n\n\nAbstract\nA crystallization of a PL $d$-manifold is a 
 certain type of edge colored graph that represents the manifold. Extending
  the notion of genus in dimension 2\, the notion of regular genus for a $d
 $-manifold has been introduced\, which is strictly related to the existenc
 e of regular embeddings of crystallizations of manifold into surfaces. The
  regular genus of a closed connected orientable (resp. non-orientable) sur
 face coincides with its genus (resp. half of its genus)\, while the regula
 r genus of a closed connected 3-manifold coincides with its Heegaard genus
 . Let $M$ be a compact connected PL 4-manifold with boundary. In this talk
 \, I shall give lower bounds for regular genus of the manifold $M$. In par
 ticular\, if $M$ is a connected compact PL $4$- manifold with $h$ boundary
  components then its regular genus $\\mathcal{G}(M)$ satisfies the followi
 ng inequalities: \n\n $\\mathcal{G}(M)\\geq 2\\chi(M)+3m+2h-4$ and $\\math
 cal{G}(M)\\geq \\mathcal{G}(\\partial M)+2\\chi(M)+2m+2h-4\,$\n\n  where $
 m$ is the rank of the fundamental group of the manifold $M$.\n
LOCATION:https://researchseminars.org/talk/CATGT/19/
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