Research

There is a motto that maps with well-behaved (by which I mean acyclic, contractible, cell-like, small etc) point inverses induce isomorphisms in Homology/Homotopy. A good example is a theorem of Vietoris (1927) in which he proves that a surjective map with acyclic point inverses induces isomorphisms in Homology.

My work is concerned with modern controlled topology versions of Vietoris' theorem and its converse. In my first year I used purely topological methods to characterise when a simplicial map has cell-like point inverses. (Which means in particular that it is a limit of homeomorphisms.) My end of first year report can be found here.

Since then I have been using chain complex methods rather than homology. In particular, I use algebraic categories to characterise maps with controlled point inverses. Using these categories one can answer such questions as 'When is a simplicial complex a homology manifold?'

Room 5401
School of Mathematics
James Clerk Maxwell Building
The King's Buildings
West Mains Road
Edinburgh
EH9 3JZ
Tel (0131) 6517670

E-mail me
S.Adams-Florou(at)sms.ed.ac.uk