%0 Journal Article %T The average dual surface of a cohomology class and minimal simplicial decompositions of infinitely many lens spaces %A Ed Swartz %J Mathematics %D 2013 %I arXiv %X Discrete normal surfaces are normal surfaces whose intersection with each tetrahedron of a triangulation has at most one component. They are also natural Poincar\'e duals to 1-cocycles with $\ZZ/2\ZZ$-coefficients. For a fixed cohomology class in a simplicial poset the average Euler characteristic of the associated discrete normal surfaces only depends on the $f$-vector of the triangulation. As an application we determine the minimum simplicial poset representations, also known as crystallizations, of lens spaces $L(2k,q),$ where $2k=qr+1.$ Higher dimensional analogs of discrete normal surfaces are closely connected to the Charney-Davis conjecture for flag spheres. %U http://arxiv.org/abs/1310.1991v2