# Minimal crystallizations of 3-manifolds

Presented by:

Basudeb Datta, Indian Institute of Science, Bangalore
Date:

Tue 18 Mar, 3:00 pm - 4:00 pm
Venue:

Building 67, Room 442 We introduce the weight of a group which has a presentation with number of relations is at most the number of generators. We show that the number of vertices of any crystallization of a connected closed 3-manifold M is at least the weight of the fundamental group of M. This lower bound is sharp for the real projective 3-space, the lens spaces L(3,1) and L(5,2), the 3-torus, S^2 x S^1, the 3-dimensional Klein bottle and S^3 / Q_8, where Q_8 is the quaternion group. Moreover, there is a unique such vertex minimal crystallizationin for each of these seven cases.

This is joint work with Biplab Basak.