Symmetric Products of Two Dimensional Complexes

Abstract

This paper exhibits a multiplicative and minimal cellular complex which allows explicit and complete (co)homological calculations for the symmetric products of a finite two dimensional CW complex. By considering cohomology, we observe that a classical theorem of Clifford on the dimension of various linear series on a projective curve has a purely topological statement. We give a "real" analog of this theorem for unoriented topological surfaces.