The average dual surface of a cohomology class and minimal simplicial decompositions of infinitely many lens spaces

Ed Swartz

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arXiv · 1310.1991

The average dual surface of a cohomology class and minimal simplicial decompositions of infinitely many lens spaces

Ed Swartz

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Abstract

Discrete normal surfaces are normal surfaces whose intersection with each tetrahedron of a triangulation has at most one component. They are also natural Poincaré 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.

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Ed Swartz. 2013-11-06. The average dual surface of a cohomology class and minimal simplicial decompositions of infinitely many lens spaces. https://arxiv.org/abs/1310.1991

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