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Symmetric Products of Two Dimensional Complexes

Sadok Kallel·Paolo Salvatore
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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.

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Sadok Kallel, Paolo Salvatore. 2005-10-09. Symmetric Products of Two Dimensional Complexes. https://arxiv.org/abs/math/0510176

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