Given an arbitrary non-zero simplicial cycle and a generic vector coloring of its vertices, there is a way to produce a graded Poincare duality algebra associated with these data. The procedure relies on the theory of volume polynomials and multi-fans. This construction includes many important examples, such as cohomol…
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New method finds hyperelliptic 4-manifolds from polytope vector-colorings.
problem Finding hyperelliptic 4-manifolds from polytope vector-colorings.
method Introducing Hamiltonian subcomplexes and their corresponding subgroups.
result For dimensions ≤ 4, there is a bijection between Hamiltonian subcomplexes and hyperelliptic involutions.