Volume 13, issue 6 (2013)

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Different moment-angle manifolds arising from two polytopes having the same bigraded Betti numbers

Suyoung Choi

Algebraic & Geometric Topology 13 (2013) 3639–3649
Abstract

Two simple polytopes of dimension $3$ having identical bigraded Betti numbers but nonisomorphic Tor–algebras are presented. These polytopes provide two homotopically different moment-angle manifolds having the same bigraded Betti numbers. These two simple polytopes are the first examples of polytopes that are (toric) cohomologically rigid but not combinatorially rigid.

Keywords
moment-angle manifold, bigraded Betti number, Tor–algebra, cohomological rigidity, combinatorial rigidity
Primary: 55N99
Secondary: 05A15