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A Finite-Geometric Obstruction and a Polytopal Separation of Buchstaber Invariants
We construct a polytopal simplicial sphere that admits a mod 2 characteristic map but no mod 3 characteristic map, and hence no integral one. This shows that the Buchstaber number of a polytopal sphere can be strictly smaller than its real Buchstaber number, and gives a negative answer to the toric
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