Abstract: 
Cylindrical algebraic decomposition (CAD) represents a semialgebraic subset of real nspace as a cell complex. For this to be of any use, practical or theoretical, we need some further conditions: a helpful one is to have a regular cell complex (in effect, one barycentric subdivision away from a simplicial complex). In general a CAD is not a regular cell complex, but, using methods from real algebraic geometry and from topology, we show that under some quite ordinary circumstances it is. This is joint work with James Davenport and Acyr Locatelli.
