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SUMMARY:Biplab Basak (Indian Institute of Technology Delhi)
DTSTART:20200729T053000Z
DTEND:20200729T063000Z
DTSTAMP:20260423T021413Z
UID:CATGT/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CATGT/3/">Th
 ree-dimensional normal pseudomanifolds with relatively few edges</a>\nby B
 iplab Basak (Indian Institute of Technology Delhi) as part of Applications
  of Combinatorics in Algebra\, Topology and Graph Theory\n\n\nAbstract\nFr
 om the Lower Bound Theorem\, we know that if $\\Delta$ is a $d$-dimensiona
 l  normal pseudomanifold then $g_2(\\Delta):= f_1(\\Delta)-(d+1)f_0(\\Delt
 a) + \\binom{d+2}{2}\\geq 0$ and equality holds if and only if $\\Delta$ i
 s a stacked sphere for $d\\geq 3$. Thus\, Lower Bound Theorem classifies n
 ormal pseudomanifolds of dimension $d\\geq 3$ with $g_2=0$. Later\, Nevo a
 nd Novinsky  have classified  homology $d$-spheres with $g_2=1$ for $d\\ge
 q 3$. Zheng has shown that  homology manifolds  of dimension $d\\geq 3$ wi
 th $g_2=2$ are polytopal spheres.  From the works of Kalai and Fogelsanger
   it follows that  $g_2(\\Delta) \\geq g_2({\\rm lk}(v\, \\Delta))$ for an
 y vertex $v$ of $\\Delta$.\n\nIn this talk\, I shall show that the topolog
 ical and combinatorial classification of  normal $3$-pseudomanifolds $\\De
 lta$ when $\\Delta$ has at most two singularity and $g_2(\\Delta) = g_2({\
 \rm lk}(v\, \\Delta))$ for some vertex $v$ of $\\Delta$. In particular\, I
  shall show that    normal $3$-pseudomanifolds with $g_2=3$ are either sph
 ere or suspension of $\\mathbb{RP}^2$.\n
LOCATION:https://researchseminars.org/talk/CATGT/3/
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