Event Type:

Department Colloquium

Date/Time:

Monday, October 31, 2011 - 09:00

Location:

Kidder 350

Guest Speaker:

Dusan Repovs

Institution:

University of Ljubljana, Slovenia

Abstract:

We shall present a survey of a classical conjecture concerning the characterization of topological n-

manifolds: the R. L. Moore conjecture from the 1930's asserts that every (finite-dimensional) cell-

like decomposition of R^n is a topological factor of R^{n+1}. The key object are so-called generalized

manifolds, i.e. Euclidean neighborhood retracts (ENR) which are also homology manifolds. We

shall look at their history, from the early beginnings to the present day, concentrating on those

geometric properties of these spaces which are particular for dimensions 3 and 4, in comparison with

generalized (n>4)-manifolds.

In the second part of the talk we shall present the current state of this - still unsettled - notoriously

difficult conjecture, listing recent results which are a joint work with D. Halverson. We shall also

explain why one must assume finite dimensionality of the quotient space (this is related to the

famous P. S. Aleksandrov problem in cohomological dimension theory which was also formulated in

the 1930's and solved only in the 1990's). Finally, we shall list open problems and conjectures.

Host: