Monday, April 16, 2007 - 9:15am - 10:05am
Saugata Basu (Georgia Institute of Technology)
I will describe some results giving a single exponential upper bound on
the number of possible homotopy types of the fibres of a Pfaffian map, in terms
of the format of its graph.
In particular,
we show that if a semi-algebraic set S ⊂ ℝm+n
is defined by a Boolean formula with s polynomials of degrees less than d, and
π: (R)m+n
(R)n is the projection
on a subspace, then the number of different homotopy types of fibres of
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