Speaker

:

 Prof. Basudeb Datta

Affiliation

:

Indian Institute of Science
 

Subject Area

:

Mathematics

Venue

:

Lecture Hall I, Dept of Mathematics

Time

:

4.00 pm

Date  

:

Friday, 24th November 2006

Title

:

Minimal triangulations of non-simply connected manifolds

In 1987, Brehm and K\"{u}hnel showed that for $d \geq
3$, any triangulation of a non-simply connected closed
$d$-manifold requires at least $2d + 3$ vertices. In 1986,
K\"{u}hnel proved that this bound is optimal by showing that
there is a $(2d + 3)$-vertex $d$-dimensional simplicial complex
(denoted by $K^{d}_{2d + 3}$) which triangulates a sphere bundle
over the circle. In a recent paper, we have shown that $K^{d}_{2d
+ 3}$ is the unique $(2d + 3)$-vertex triangulation of a
non-simply connected closed $d$-manifold for all $d \geq 3$. In
this talk, I would like to present an outline of the proof of our
main result together with some constructions.