Numerical invariants of links in 3-manifolds

1983 ◽  
pp. 285-304
Author(s):  
Richard Mandelbaum ◽  
Boris Moishezon
Keyword(s):  
Numerical Invariants

Homotopy invariants and continuous mappings

1950 ◽  
Vol 202 (1069) ◽  
pp. 253-263 ◽  
Keyword(s):  
Homotopy Type ◽  
Betti Numbers ◽  
Continuous Mappings ◽  
Numerical Invariants ◽  
Homotopy Invariants

This paper contributes new numerical invariants to the topology of a certain class of polyhedra. These invariants, together with the Betti numbers and coefficients of torsion, characterize the homotopy type of one of these polyhedra. They are also applied to the classification of continuous mappings of an ( n + 2)-dimensional polyhedron into an ( n + 1)-sphere ( n > 2).

THE JACOBSON GRAPH OF COMMUTATIVE RINGS

2012 ◽  
Vol 12 (03) ◽  
pp. 1250179 ◽  
Author(s):  
A. AZIMI ◽  
A. ERFANIAN ◽  
M. FARROKHI D. G.
Keyword(s):  
Commutative Ring ◽  
Chromatic Number ◽  
Independence Number ◽  
Commutative Rings ◽  
Dominating Number ◽  
Jacobson Graph ◽  
Vertex Set ◽  
Numerical Invariants ◽  
Nonzero Identity

Let R be a commutative ring with nonzero identity. Then the Jacobson graph of R, denoted by 𝔍R, is defined as a graph with vertex set R\J(R) such that two distinct vertices x and y are adjacent if and only if 1 - xy is not a unit of R. We obtain some graph theoretical properties of 𝔍R including its connectivity, planarity and perfectness and we compute some of its numerical invariants, namely diameter, girth, dominating number, independence number and vertex chromatic number and give an estimate for its edge chromatic number.

Local Bounds for Torsion Points on Abelian Varieties

2008 ◽  
Vol 60 (3) ◽  
pp. 532-555 ◽  
Author(s):  
Pete L. Clark ◽  
Xavier Xarles
Keyword(s):  
Abelian Varieties ◽  
Residue Field ◽  
Rational Numbers ◽  
Abelian Surface ◽  
Torsion Subgroup ◽  
Good Reduction ◽  
Torsion Points ◽  
Ramification Index ◽  
Numerical Invariants ◽  
Split Torus

AbstractWe say that an abelian variety over a p-adic field K has anisotropic reduction (AR) if the special fiber of its Néronminimal model does not contain a nontrivial split torus. This includes all abelian varieties with potentially good reduction and, in particular, those with complex or quaternionic multiplication. We give a bound for the size of the K-rational torsion subgroup of a g-dimensional AR variety depending only on g and the numerical invariants of K (the absolute ramification index and the cardinality of the residue field). Applying these bounds to abelian varieties over a number field with everywhere locally anisotropic reduction, we get bounds which, as a function of g, are close to optimal. In particular, we determine the possible cardinalities of the torsion subgroup of an AR abelian surface over the rational numbers, up to a set of 11 values which are not known to occur. The largest such value is 72.

scholarly journals Algebraic Surfaces of General Type with Small c21 in Positive Characteristic

2008 ◽  
Vol 191 ◽  
pp. 111-134 ◽  
Author(s):  
Christian Liedtke
Keyword(s):  
Characteristic Zero ◽  
General Type ◽  
Positive Characteristic ◽  
Algebraic Surfaces ◽  
Surfaces Of General Type ◽  
Arbitrary Characteristic ◽  
Numerical Invariants ◽  
Characteristic 2

AbstractWe establish Noether’s inequality for surfaces of general type in positive characteristic. Then we extend Enriques’ and Horikawa’s classification of surfaces on the Noether line, the so-called Horikawa surfaces. We construct examples for all possible numerical invariants and in arbitrary characteristic, where we need foliations and deformation techniques to handle characteristic 2. Finally, we show that Horikawa surfaces lift to characteristic zero.

Numerical Invariants in Homotopical Algebra, I

1975 ◽  
Vol 27 (4) ◽  
pp. 901-934 ◽  
Author(s):  
K. Varadarajan
Keyword(s):  
Homotopy Theory ◽  
Algebra I ◽  
Homotopical Algebra ◽  
Numerical Invariants ◽  
Set Up ◽  
Lusternik Schnirelmann ◽  
Classical Homotopy

Classically CW-complexes were found to be the best suited objects for studying problems in homotopy theory. Certain numerical invariants associated to a CW-complex X such as the Lusternik-Schnirelmann Category of X, the index of nilpotency of ᘯ(X), the cocategory of X, the index of conilpotency of ∑ (X) have been studied by Eckmann, Hilton, Berstein and Ganea, etc. Recently D. G. Quillen [6] has developed homotopy theory for categories satisfying certain axioms. In the axiomatic set up of Quillen the duality observed in classical homotopy theory becomes a self-evident phenomenon, the axioms being so formulated.

scholarly journals Some Eccentricity-Based Topological Indices and Polynomials of Poly(EThyleneAmidoAmine) (PETAA) Dendrimers

Processes ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 433 ◽  
Author(s):  
Jialin Zheng ◽  
Zahid Iqbal ◽  
Asfand Fahad ◽  
Asim Zafar ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
Molecular Descriptors ◽  
Molecular Graph ◽  
Topological Indices ◽  
Molecular Structures ◽  
Connectivity Index ◽  
Connectivity Indices ◽  
Numerical Invariants ◽  
Explicit Representations ◽  
Pharmaceutical Properties

Topological indices have been computed for various molecular structures over many years. These are numerical invariants associated with molecular structures and are helpful in featuring many properties. Among these molecular descriptors, the eccentricity connectivity index has a dynamic role due to its ability of estimating pharmaceutical properties. In this article, eccentric connectivity, total eccentricity connectivity, augmented eccentric connectivity, first Zagreb eccentricity, modified eccentric connectivity, second Zagreb eccentricity, and the edge version of eccentric connectivity indices, are computed for the molecular graph of a PolyEThyleneAmidoAmine (PETAA) dendrimer. Moreover, the explicit representations of the polynomials associated with some of these indices are also computed.

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