Dehn-Sommerville manifolds form a broad class of finite simplicial complexes that the paper claims to endow with Dehn-Sommerville face symmetries, level-set closure, chromatic bound 2q+2, and monoid closure under joins.
Characteristic Topological Invariants
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abstract
The higher characteristics w_m(G) for a finite abstract simplicial complex G are topological invariants that satisfy k-point Green function identities and can be computed in terms of Euler characteristic in the case of closed manifolds, where we give a new proof of w_m(G)=w_1(G). Also the sphere formula generalizes: for any simplicial complex, the total higher characteristics of unit spheres at even dimensional simplices is equal to the total higher characteristic of unit spheres at odd dimensional simplices.
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Dehn Sommerville Manifolds
Dehn-Sommerville manifolds form a broad class of finite simplicial complexes that the paper claims to endow with Dehn-Sommerville face symmetries, level-set closure, chromatic bound 2q+2, and monoid closure under joins.