scholarly journals Example of C-rigid polytopes which are not B-rigid

2019 ◽  
Vol 69 (2) ◽  
pp. 437-448
Author(s):  
Suyoung Choi ◽  
Kyoungsuk Park
Keyword(s):  
Cohomology Ring ◽  
Combinatorial Structure ◽  
Simple Polytope ◽  
Quasitoric Manifold

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.

scholarly journals Toric objects associated with the dodecahedron

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2329-2356
Author(s):  
Djordje Baralic ◽  
Jelena Grbic ◽  
Ivan Limonchenko ◽  
Aleksandar Vucic
Keyword(s):  
Homotopy Theory ◽  
Cohomology Ring ◽  
Massey Products ◽  
Small Cover ◽  
Toric Topology ◽  
Quasitoric Manifold

In this paper we illustrate a tight interplay between homotopy theory and combinatorics within toric topology by explicitly calculating homotopy and combinatorial invariants of toric objects associated with the dodecahedron. In particular, we calculate the cohomology ring of the (complex and real) moment-angle manifolds over the dodecahedron, and of a certain quasitoric manifold and of a related small cover. We finish by studying Massey products in the cohomology ring of moment-angle manifolds over the dodecahedron and how the existence of nontrivial Massey products influences the behaviour of the Poincar? series of the corresponding Pontryagin algebra.

Combinatorial Design of Molecule using Activity-Linked Substructural Topological Information as Applied to Antitubercular Compounds

2018 ◽  
Vol 15 (1) ◽  
pp. 67-81 ◽  
Author(s):  
Chandan Raychaudhury ◽  
Md. Imbesat Hassan Rizvi ◽  
Debnath Pal
Keyword(s):  
Biological Activities ◽  
Combinatorial Design ◽  
Combinatorial Structure ◽  
Potential Drug ◽  
Structure Generation ◽  
Topological Information ◽  
Active Compounds ◽  
Antitubercular Drugs ◽  
Topological Distance ◽  
Drug Molecules

Background: Generating a large number of compounds using combinatorial methods increases the possibility of finding novel bioactive compounds. Although some combinatorial structure generation algorithms are available, any method for generating structures from activity-linked substructural topological information is not yet reported. Objective: To develop a method using graph-theoretical techniques for generating structures of antitubercular compounds combinatorially from activity-linked substructural topological information, predict activity and prioritize and screen potential drug candidates. </P><P> Methods: Activity related vertices are identified from datasets composed of both active and inactive or, differently active compounds and structures are generated combinatorially using the topological distance distribution associated with those vertices. Biological activities are predicted using topological distance based vertex indices and a rule based method. Generated structures are prioritized using a newly defined Molecular Priority Score (MPS). Results: Studies considering a series of Acid Alkyl Ester (AAE) compounds and three known antitubercular drugs show that active compounds can be generated from substructural information of other active compounds for all these classes of compounds. Activity predictions show high level of success rate and a number of highly active AAE compounds produced high MPS score indicating that MPS score may help prioritize and screen potential drug molecules. A possible relation of this work with scaffold hopping and inverse Quantitative Structure-Activity Relationship (iQSAR) problem has also been discussed. The proposed method seems to hold promise for discovering novel therapeutic candidates for combating Tuberculosis and may be useful for discovering novel drug molecules for the treatment of other diseases as well.

A Generalization of “Concordance of PL-Homeomorphisms of Sp × Sq

1972 ◽  
Vol 24 (3) ◽  
pp. 426-431 ◽  
Author(s):  
J. P. E. Hodgson
Keyword(s):  
Equivalence Relation ◽  
Cohomology Ring

Let Mm be a closed PL manifold of dimension m. Then a concordance between two PL-homeomorphisms h0, h1:M → M is a PL-homeomorphismH: M × I → M × I such that H|M × 0 = h0 and H|M × 1 = h. Concordance is an equivalence relation and in his paper [2], M. Kato classifies PL-homeomorphisms of Sp × Sq up to concordance. To do this he treats first the problem of classifying those homeomorphisms that induce the identity in homology, and then describes the automorphisms of the cohomology ring that can arise from homeomorphisms of Sp × Sq. In this paper we show that for sufficiently connected PL-manifolds that embed in codimension 1, one can extend Kato's classification of the homeomorphisms that induce the identity in homology.

scholarly journals The existence of generating families for the cohomology ring of a graph

2003 ◽  
Vol 174 (1) ◽  
pp. 115-153 ◽  
Author(s):  
Victor Guillemin ◽  
Catalin Zara
Keyword(s):  
Cohomology Ring

Resolution of T. Ward's Question and the Israel–Finch Conjecture: Precise Analysis of an Integer Sequence Arising in Dynamics

2014 ◽  
Vol 24 (1) ◽  
pp. 195-215
Author(s):  
JEFFREY GAITHER ◽  
GUY LOUCHARD ◽  
STEPHAN WAGNER ◽  
MARK DANIEL WARD
Keyword(s):  
Weighted Average ◽  
Analytic Number Theory ◽  
Combinatorial Structure ◽  
Asymptotic Growth ◽  
First Order ◽  
Integer Sequence ◽  
Precise Analysis ◽  
Formula Group ◽  
Fourth Author ◽  
Image Position

We analyse the first-order asymptotic growth of \[ a_{n}=\int_{0}^{1}\prod_{j=1}^{n}4\sin^{2}(\pi jx)\, dx. \] The integer an appears as the main term in a weighted average of the number of orbits in a particular quasihyperbolic automorphism of a 2n-torus, which has applications to ergodic and analytic number theory. The combinatorial structure of an is also of interest, as the ‘signed’ number of ways in which 0 can be represented as the sum of ϵjj for −n ≤ j ≤ n (with j ≠ 0), with ϵj ∈ {0, 1}. Our result answers a question of Thomas Ward (no relation to the fourth author) and confirms a conjecture of Robert Israel and Steven Finch.

The polynomial cohomology ring for characteristicp

1962 ◽  
Vol 79 (1) ◽  
pp. 297-306
Author(s):  
Robert Heaton
Keyword(s):  
Cohomology Ring
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