scholarly journals Classification of $SO(n)$ -bundles over the quaternion projective plane

1963 ◽  
Vol 15 (1) ◽  
pp. 69-74
Author(s):  
Seiya SASAO ◽  
Itiro TAMURA
Keyword(s):  
Projective Plane

Cohomology of Homotopy 2-types

2019 ◽  
pp. 379-422
Author(s):  
Graham Ellis
Keyword(s):  
Perturbation Theory ◽  
Projective Plane ◽  
Integral Homology ◽  
Homotopy Classes ◽  
Cw Complex ◽  
Crossed Modules ◽  
Homological Perturbation Theory ◽  
Homological Perturbation ◽  
Manual Classification

This chapter introduces some of the basic ingredients in the classification of homotopy 2-types and describes datatypes and algorithms for implementing them on a computer. These are illustrated using computer examples involving: the fundamental crossed modules of a CW-complex, cat-1-groups, simplicial groups, Moore complexes, the Dold-Kan correspondence, integral homology of simplicial groups, homological perturbation theory. A manual classification of homotopy classes of maps from a surface to the projective plane is also included.

scholarly journals Real Hypersurfaces of Nonflat Complex Projective Planes Whose Jacobi Structure Operator Satisfies a Generalized Commutative Condition

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Theocharis Theofanidis
Keyword(s):  
Projective Plane ◽  
Projective Planes ◽  
Additional Restriction ◽  
Real Hypersurfaces ◽  
Specific Function ◽  
Complex Projective Plane ◽  
Jacobi Structure ◽  
Complex Projective

Real hypersurfaces satisfying the conditionϕl=lϕ(l=R(·,ξ)ξ)have been studied by many authors under at least one more condition, since the class of these hypersurfaces is quite tough to be classified. The aim of the present paper is the classification of real hypersurfaces in complex projective planeCP2satisfying a generalization ofϕl=lϕunder an additional restriction on a specific function.

scholarly journals Applications of the Projective Plane in Coding Theory

2020 ◽  
Vol 55 (1) ◽  
Author(s):  
Najm Abdulzahra Makhrib Al-Seraji ◽  
Zainab Sadiq Jafar
Keyword(s):  
Projective Plane ◽  
Coding Theory ◽  
Minimum Distance ◽  
Incidence Matrix ◽  
Galois Field ◽  
Programming System ◽  
Combinatorial Structures

The goal of this paper was to study the applications of the projective plane PG (2, q) over a Galois field of order q in the projective linear (n, k, d, q) -code such that the parameters length of code n, the dimension of code k, and the minimum distance d with the error-correcting e according to an incidence matrix have been calculated. Also, this research provides examples and theorems of links between the combinatorial structures and coding theory. The calculations depend on the GAP (groups, algorithms, and programming) system. The method of the research depends on the classification of the points and lines in PG (2, q).

Classification of surfaces of general type with Euler number 3

2013 ◽  
Vol 2013 (679) ◽  
pp. 1-22 ◽  
Author(s):  
Sai-Kee Yeung
Keyword(s):  
Projective Plane ◽  
Recent Work ◽  
Present Article ◽  
Smooth Surface ◽  
General Type ◽  
Euler Number ◽  
Projective Planes ◽  
Surfaces Of General Type ◽  
Surface Of General Type

Abstract The smallest topological Euler–Poincaré characteristic supported on a smooth surface of general type is 3. In this paper, we show that such a surface has to be a fake projective plane unless h1, 0(M) = 1. Together with the classification of fake projective planes given by Prasad and Yeung, the recent work of Cartwright and Steger, and a proof of the arithmeticity of the lattices involved in the present article, this gives a classification of such surfaces.

scholarly journals Classification of the Hyperovals in PG(2,64)

10.37236/7589 ◽  
2019 ◽  
Vol 26 (2) ◽  
Author(s):  
Peter Vandendriessche
Keyword(s):  
Projective Plane ◽  
Finite Projective Plane ◽  
Point Sets ◽  
Incidence Structures ◽  
Isomorphism Classes ◽  
Full Classification

In this paper, we present a full classification of the hyperovals in the finite projective plane $\mathrm{PG}(2,64)$, showing that there are exactly 4 isomorphism classes. The techniques developed to obtain this result can be applied more generally to classify point sets with $0$ or $2$ points on every line, in a broad range of highly symmetric incidence structures.

scholarly journals On the disposition of cubic and pair of conics in a real projective plane

2020 ◽  
Vol 22 (1) ◽  
pp. 24-37
Author(s):  
Victoriya A. Gorskaya ◽  
Grigory M. Polotovskiy
Keyword(s):  
Projective Plane ◽  
General Position ◽  
Algebraic Curves ◽  
Hilbert Problem ◽  
Topological Classification ◽  
Real Projective Plane ◽  
16Th Hilbert Problem ◽  
Algebraic Manifolds ◽  
Manifolds With Singularities

In the first part of the 16th Hilbert problem the question about the topology of nonsingular projective algebraic curves and surfaces was formulated. The problem on topology of algebraic manifolds with singularities belong to this subject too. The particular case of this problem is the study of curves that are decompozable into the product of curves in a general position. This paper deals with the problem of topological classification of mutual positions of a nonsingular curve of degree three and two nonsingular curves of degree two in the real projective plane. Additiolal conditions for this problem include general position of the curves and its maximality; in particular, the number of common points for each pair of curves-factors reaches its maximum. It is proved that the classification contains no more than six specific types of positions of the species under study. Four position types are built, and the question of realizability of the two remaining ones is open.

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