Lower bounds¶for the relative Lusternik-Schnirelmann category

2000 ◽  
Vol 101 (4) ◽  
pp. 533-542 ◽  
Author(s):  
Pierre-Marie Moyaux
Keyword(s):  
Lower Bounds ◽  
Lusternik Schnirelmann

scholarly journals Triangulations with few vertices of manifolds with non-free fundamental group

2019 ◽  
Vol 149 (6) ◽  
pp. 1453-1463
Author(s):  
Petar Pavešić
Keyword(s):  
Fundamental Group ◽  
Lower Bounds ◽  
Category Theory ◽  
Homology Sphere ◽  
Dimensional Manifold ◽  
Lusternik Schnirelmann ◽  
Few Vertices

AbstractWe study lower bounds for the number of vertices in a PL-triangulation of a given manifold M. While most of the previous estimates are based on the dimension and the connectivity of M, we show that further information can be extracted by studying the structure of the fundamental group of M and applying techniques from the Lusternik-Schnirelmann category theory. In particular, we prove that every PL-triangulation of a d-dimensional manifold (d ⩾ 3) whose fundamental group is not free has at least 3d + 1 vertices. As a corollary, every d-dimensional homology sphere that admits a combinatorial triangulation with less than 3d vertices is PL-homeomorphic to Sd. Another important consequence is that every triangulation with small links of M is combinatorial.

scholarly journals LS-category of moment-angle manifolds and higher order Massey products

2021 ◽  
Vol 33 (5) ◽  
pp. 1179-1205
Author(s):  
Piotr Beben ◽  
Jelena Grbić
Keyword(s):  
Simplicial Complex ◽  
Structural Properties ◽  
Lower Bounds ◽  
Higher Order ◽  
Hyperbolic Manifolds ◽  
Upper And Lower Bounds ◽  
Connected Sum ◽  
Massey Products ◽  
Higher Dimensional ◽  
Lusternik Schnirelmann

Abstract Using the combinatorics of the underlying simplicial complex K, we give various upper and lower bounds for the Lusternik–Schnirelmann (LS) category of moment-angle complexes 𝒵 K {\mathcal{Z}_{K}} . We describe families of simplicial complexes and combinatorial operations which allow for a systematic description of the LS-category. In particular, we characterize the LS-category of moment-angle complexes 𝒵 K {\mathcal{Z}_{K}} over triangulated d-manifolds K for d ≤ 2 {d\leq 2} , as well as higher-dimensional spheres built up via connected sum, join, and vertex doubling operations. We show that the LS-category closely relates to vanishing of Massey products in H * ⁢ ( 𝒵 K ) {H^{*}(\mathcal{Z}_{K})} , and through this connection we describe first structural properties of Massey products in moment-angle manifolds. Some of the further applications include calculations of the LS-category and the description of conditions for vanishing of Massey products for moment-angle manifolds over fullerenes, Pogorelov polytopes and k-neighborly complexes, which double as important examples of hyperbolic manifolds.

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Lower bounds on the dimension of the Rauzy gasket

2020 ◽  
Vol 148 (2) ◽  
pp. 321-327
Author(s):  
Rodolfo Gutiérrez-Romo ◽  
Carlos Matheus
Keyword(s):  
Lower Bounds

A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

10.37236/1188 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers

For $k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$ and on the k-color Ramsey numbers of $K_3$.

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