Department of Mathematics

Indian Institute of Science

Bangalore 560 012

 

GOLDEN JUBILEE YEAR 2005 - 2006

SEMINAR.....

Speaker

:

Prof. Basudeb Datta

 

Affiliation

:

Department of Mathematics

Indian Institute of Science
Bangalore

 

Subject Area

:

Mathematics

 

Venue

:

Lecture Hall I, Dept of Mathematics

 

Time

:

4.00 pm

 

Date  

:

December 09, 2005

 

Event Title1

:

"Minimal Triangulations of Manifolds"

 

Abstract  

 

Aiming at a complete classification of objects like algebraic varities,Henri Poincare defined triangulation in 1895 and asked the following. (i) Is there a triangulation for every algebraic varity? (ii) s there a triangulation for every topological manifold? In 1935, Cairns proved that each closed smooth manifold is triangulable. In 1964, Lojaciewitz proved that each real algebraic variety is triangulable. But, it took 100 years to find a non-triangulable manifold. In 1985, Casson showed that there exists a topological 4-manifold which is not triangulable.

In this talk, we are interested on minimal triangulations of pl-manifolds. We present a brief survey on the works done in last 25 years on the following: (i) Finding the minimal number of vertices required to triangulate a given pl-manifold. (ii) Given positive integers $n$ and $d$, construction of $n$-vertex triangulations of different $d$-dimensional pl-manifolds. (iii) Classifications of all the triangulations of a given pl-manifold with same number of vertices.
 


Contact: +91 (80) 2293 2711, +91 (80) 2293 2625
E-mail: chairman.math[at]iisc[dot]ac[dot]in