A simple polytope P is said to be B-rigid if its combinatorial structure is characterized by its Tor-Algebra, and is said to be C-rigid if its combinatorial structure is characterized by the cohomology ring of a quasitoric manifold over P. It is known that a B-rigid simple polytope is C-rigid. In this paper, we show that the B-rigidity is not equivalent to the C-rigidity.
2010 M a t h e m a t i c s S u b j e c t C l a s s i f i c a t i o n: 52B35, 14M25, 05E40, 55NXX. Keywords: cohomologically rigid, B-rigid, quasitoric manifold, simple polytope, Peterson graph. The first named author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT & Future Planning(NRF-2016R1D1A1A09917654).
