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

Choi, Suyoung

doi:10.2140/agt.2013.13.3639

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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

DOI: 10.2140/agt.2013.13.3639

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

Mathematical Subject Classification 2010

Primary: 55N99

Secondary: 05A15

References

Publication

Received: 31 July 2012

Revised: 4 June 2013

Accepted: 5 June 2013

Published: 14 October 2013

Authors

Suyoung Choi
Department of Mathematics Ajou University San 5, Woncheon-dong, Yeongtong-gu Suwon 443-749 South Korea

Volume 13, issue 6 (2013)