Toric Topology

2008 ◽  
Keyword(s):  
Toric Topology

Toric Topology

2015 ◽  
Author(s):  
Victor Buchstaber ◽  
Taras Panov
Keyword(s):  
Toric Topology

scholarly journals Categorical aspects of toric topology

2008 ◽  
pp. 293-322 ◽  
Author(s):  
Taras E. Panov ◽  
Nigel Ray
Keyword(s):  
Toric Topology

scholarly journals A new graph invariant arises in toric topology

2015 ◽  
Vol 67 (2) ◽  
pp. 699-720 ◽  
Author(s):  
Suyoung CHOI ◽  
Hanchul PARK
Keyword(s):  
Graph Invariant ◽  
Toric Topology

scholarly journals Massey products, toric topology and combinatorics of polytopes

2019 ◽  
Vol 83 (6) ◽  
pp. 1081-1136
Author(s):  
V. M. Buchstaber ◽  
I. Yu. Limonchenko
Keyword(s):  
Massey Products ◽  
Toric Topology

scholarly journals Rigidity problems in toric topology: A survey

2011 ◽  
Vol 275 (1) ◽  
pp. 177-190 ◽  
Author(s):  
Suyoung Choi ◽  
Mikiya Masuda ◽  
Dong Youp Suh
Keyword(s):  
Toric Topology ◽  
Rigidity Problems

scholarly journals On the Equivalence of B-Rigidity and C-Rigidity for Quasitoric Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Jin Hong Kim
Keyword(s):  
Convex Polytopes ◽  
Cohomology Rings ◽  
Toric Topology ◽  
Quasitoric Manifolds ◽  
Simple Convex ◽  
Cohomological Rigidity

For quasitoric manifolds and moment-angle complexes which are central objects recently much studied in toric topology, there are several important notions of rigidity formulated in terms of cohomology rings. The aim of this paper is to show that, among other things, Buchstaber-rigidity (or B-rigidity) is equivalent to cohomological-rigidity (or C-rigidity) for simple convex polytopes supporting quasitoric manifolds.

scholarly journals Wedge Operations and Torus Symmetries II

2017 ◽  
Vol 69 (4) ◽  
pp. 767-789 ◽  
Author(s):  
Suyoung Choi ◽  
Hanchul Park
Keyword(s):  
Positive Integer ◽  
Simplicial Complex ◽  
Main Idea ◽  
Picard Number ◽  
Fundamental Idea ◽  
Combinatorial Objects ◽  
Toric Topology ◽  
Simplicial Sphere ◽  
Fixed Positive Integer

AbstractA fundamental idea in toric topology is that classes of manifolds with well-behaved torus actions (simply, toric spaces) are classified by pairs of simplicial complexes and (non-singular) characteristic maps. In a previous paper, the authors provided a new way to find all characteristic maps on a simplicial complex K(J) obtainable by a sequence of wedgings from K.The main idea was that characteristic maps on K theoretically determine all possible characteristic maps on a wedge of K.We further develop our previous work for classification of toric spaces. For a star-shaped simplicial sphere K of dimension n-1 with m vertices, the Picard number Pic(K) of K is m-n. We call K a seed if K cannot be obtained by wedgings. First, we show that for a fixed positive integer 𝓁, there are at most finitely many seeds of Picard 𝓁 number supporting characteristic maps. As a corollary, the conjecture proposed by V. V. Batyrev in is solved affirmatively.Secondly, we investigate a systematicmethod to find all characteristic maps on K(J) using combinatorial objects called (realizable) puzzles that only depend on a seed K. These two facts lead to a practical way to classify the toric spaces of fixed Picard number.

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.

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