Example of C-rigid polytopes which are not B-rigid
-
Suyoung Choi
and
Kyoungsuk Park
Abstract
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.
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).
(Communicated by David Buhagiar)
Acknowledgement
The authors thank the anonymous reviewer for his/her careful reading of our manuscript and pointing out some computation errors in the proof of the main theorem. They also appreciate the reviewer’s comments on the references and the definition of B-rigidity.
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© 2019 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Regular papers
- RNDr. Miloslav Duchoň, DrSc. passed away ∗ aug. 21, 1932 – †dec. 31, 2018
- Prof. RNDr. Gejza Wimmer, DrSc. – A Septuagenerian?
- Two monads on the category of graphs
- Entropy of MV-algebraic dynamical systems: An example
- Going up and lying over in congruence-modular algebras
- The minimal arity of near unanimity polymorphisms
- On the logarithmic derivative of zeta functions for compact even-dimensional locally symmetric spaces of real rank one
- The generalized Fermat Conjecture
- Evaluation of sums involving products of Gaussian q-binomial coefficients with applications
- Integrals of logarithmic functions and alternating multiple zeta values
- An abelian subextension of the dyadic division field of a hyperelliptic Jacobian
- The class of all semigroups related to semihypergroups of order 2
- Criterion for the weak potency of certain HNN extensions
- Fekete Szegö theorem for a close-to-convex error function
- Bounds for distance between eigenvalues of boundary value problems with retarded argument
- Gradient estimates for a nonlinear heat equation under the Finsler-Ricci flow
- Weak module amenability of triangular banach algebras II
- Some consequences of quasicentral approximate units modulo Hilbert-Schmidt class
- Example of C-rigid polytopes which are not B-rigid
- Some comments on rU-spaces
- On the equivalence of various definitions of mixed poisson processes
- A note on discrete C-embedded subspaces
