Number of two-dimensional irreducible representations of the fundamental group of a curve over a finite field

1982 ◽  
Vol 15 (4) ◽  
pp. 294-295 ◽  
Author(s):  
V. G. Drinfel'd
Keyword(s):  
Finite Field ◽  
Fundamental Group ◽  
Irreducible Representations ◽  
Two Dimensional

scholarly journals Abelianity Conjecture for Special Compact Kähler 3-Folds

2013 ◽  
Vol 57 (1) ◽  
pp. 55-78 ◽  
Author(s):  
Fréderic Campana ◽  
Benoît Claudon
Keyword(s):  
Fundamental Group ◽  
Ricci Curvature ◽  
Minimal Model ◽  
Classification Theory ◽  
Canonical Bundle ◽  
Two Dimensional ◽  
Basic Properties

AbstractUsing orbifold metrics of the appropriately signed Ricci curvature on orbifolds with a negative or numerically trivial canonical bundle and the two-dimensional log minimal model programme, we prove that the fundamental group of special compact Kähler 3-folds is almost abelian. This property was conjectured in all dimensions by Campana in 2004, and also for orbifolds in 2007, where the notion of specialness was introduced. We briefly recall the definition, basic properties and the role of special manifolds in classification theory.

Theory of Representations for Tensor Functions—A Unified Invariant Approach to Constitutive Equations

1994 ◽  
Vol 47 (11) ◽  
pp. 545-587 ◽  
Author(s):  
Q.-S. Zheng
Keyword(s):  
Mechanical Behavior ◽  
Constitutive Equations ◽  
Constitutive Laws ◽  
Irreducible Representations ◽  
Two Dimensional ◽  
Applied Mechanics ◽  
Invariant Formulation ◽  
Physical Spaces ◽  
Anisotropic Tensor ◽  
Invariant Approach

Representations in complete and irreducible forms for tensor functions allow general consistent invariant forms of the nonlinear constitutive equations and specify the number and type of the scalar variables involved. They have proved to be even more pertinent in attempts to model mechanical behavior of anisotropic materials, since here invariant conditions predominate and the number and type of independent scalar variables cannot be found by simple arguments. In the last few years, the theory of representations for tensor functions has been well established, including three fundamental principles, a number of essential theorems and a large amount of complete and irreducible representations for both isotropic and anisotropic tensor functions in three- and two-dimensional physical spaces. The objective of the present monograph is to summarize and recapitulate the up-to-date developments and results in the theory of representations for tensor functions for the convenience of further applications in contemporary applied mechanics. Some general topics on unified invariant formulation of constitutive laws are investigated.

An algebraic criterion for symmetric Hopf bifurcation

1993 ◽  
Vol 440 (1910) ◽  
pp. 727-732 ◽  
Keyword(s):  
Fixed Point ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Spherical Harmonics ◽  
Irreducible Representations ◽  
Two Dimensional ◽  
Bifurcation Theorem ◽  
Algebraic Criterion ◽  
Equivariant Hopf Bifurcation

The equivariant Hopf bifurcation theorem states that bifurcating branches of periodic solutions with certain symmetries exist when the fixed-point subspace of that subgroup of symmetries is two dimensional. We show that there is a group-theoretic restriction on the subgroup of symmetries in order for that subgroup to have a two-dimensional fixed-point subspace in any representation. We illustrate this technique for all irreducible representations of SO(3) on the space V l of spherical harmonics for l even.

REPRESENTATIONS OF THE UNITARY GROUP AND WAVE FUNCTIONS

1961 ◽  
Vol 39 (4) ◽  
pp. 510-513
Author(s):  
H. A. Venables
Keyword(s):  
Spherical Harmonics ◽  
Unitary Group ◽  
Wave Functions ◽  
Irreducible Representations ◽  
Two Dimensional

A number of wave functions besides the spherical harmonics are obtainable from the irreducible representations of the two-dimensional unitary group.

scholarly journals Casson's invariant and surgery on knots

1992 ◽  
Vol 35 (3) ◽  
pp. 383-395 ◽  
Author(s):  
C. D. Frohman ◽  
D. D. Long
Keyword(s):  
Fundamental Group ◽  
Irreducible Representations ◽  
Homology Sphere

We show that given a knot in a homology sphere there is a sequence of invariants with the property that if the nth invariant does not vanish, then this implies the existence of a family of irreducible representations of the fundamental group of the complement of the knot into SU(n).

scholarly journals Inverse monoids and immersions of 2-Complexes

2015 ◽  
Vol 25 (01n02) ◽  
pp. 301-323 ◽  
Author(s):  
John Meakin ◽  
Nóra Szakács
Keyword(s):  
Topological Space ◽  
Fundamental Group ◽  
Conjugacy Classes ◽  
Inverse Monoid ◽  
Two Dimensional ◽  
Inverse Monoids ◽  
Mild Conditions ◽  
Cw Complex ◽  
Cw Complexes

It is well known that under mild conditions on a connected topological space 𝒳, connected covers of 𝒳 may be classified via conjugacy classes of subgroups of the fundamental group of 𝒳. In this paper, we extend these results to the study of immersions into two-dimensional CW-complexes. An immersion f : 𝒟 → 𝒞 between CW-complexes is a cellular map such that each point y ∈ 𝒟 has a neighborhood U that is mapped homeomorphically onto f(U) by f. In order to classify immersions into a two-dimensional CW-complex 𝒞, we need to replace the fundamental group of 𝒞 by an appropriate inverse monoid. We show how conjugacy classes of the closed inverse submonoids of this inverse monoid may be used to classify connected immersions into the complex.

Sign in / Sign up

Export Citation Format

Share Document