Related papers: General Bourgin-Yang theorems

Let $V$ and $W$ be orthogonal representations of $G$ with $V^G= W^G=\{0\}$. Let $S(V )$ be the sphere of $V$ and $f : S(V ) \to W$ be a $G$-equivariant mapping. We give an estimate for the dimension of the set $Z_f=f^{-1}\{0\}$ in terms of…

We describe a connective $K$-theory Borsuk--Ulam/Bourgin--Yang theorem for cyclic groups of order a power of a prime $p$. Consider two finite dimensional complex representations $U$ and $V$ of the cyclic group $Z /p^{k+1}$ of order…

The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a…

We generalize Gaeta's Theorem to the family of determinantal schemes. In other words, we show that the schemes defined by minors of a fixed size of a matrix with polynomial entries belong to the same G-biliaison class of a complete…

Various gauge invariant but non-Yang-Mills dynamical models are discussed: Pr\'ecis of Chern-Simons theory in (2+1)-dimensions and reduction to (1+1)-dimensional B-F theories; gauge theories for (1+1)-dimensional gravity-matter…

After a brief review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, we present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus in two…

This paper is devoted to a systematic discussion of the supersymmetric index Tr (-1)^F for the minimal supersymmetric Yang-Mills theory -- with any simple gauge group G -- primarily in four spacetime dimensions. The index has refinements…

Generalized Yang-Mills theories have a covariant derivative that employs both scalar and vector bosons. Here we show how grand unified theories of the electroweak and strong interactions can be constructed with them. In particular the SU(5)…

Let $p$ be a prime integer, $k$ be a $p$-closed field of characteristic $\neq p$, $T$ be a torus defined over $k$, $F$ be a finite $p$-group, and $1\to T \to G \to F \to 1$ be an exact sequence of algebraic groups. Extending earlier work of…

We first extend Generalized Differential Calculus (GDC) to higher structures and create generalized G-invariant bilinear forms. In addition, we also focus on developing generalized 2- and 3-connection theories in the framework of GDC. Then,…

We show the equivalence between one-way reflections and relative projective representations. We construct generalized Goulden-Yong duals using reverse Garside element actions and folded chord diagrams. We give two applications of the…

In generalized Yang-Mills theories scalar fields can be gauged just as vector fields in a usual Yang-Mills theory, albeit it is done in the spinorial representation. The presentation of these theories is aesthetic in the following sense: A…

We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF…

We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the…

A gauge and diffeomorphism invariant theory in (2+1)-dimensions is presented in both first and second order Lagrangian form as well as in a Hamiltonian form. For gauge group $SO(1,2)$, the theory is shown to describe ordinary Einstein…

GKM theory is a powerful tool in equivariant topology and geometry that can be used to generalize classical ideas from (quasi)toric manifolds to more general torus actions. After an introduction to the topic this survey focuses on recent…

Several years ago, it was proposed that the usual solutions of the Yang-Baxter equation associated to Lie groups can be deduced in a systematic way from four-dimensional gauge theory. In the present paper, we extend this picture, fill in…

In this paper we continue our study of the thermodynamics of large N gauge theories on compact spaces. We consider toroidal compactifications of pure SU(N) Yang-Mills theories and of maximally supersymmetric Yang-Mills theories…

We establish a generic formula for the generalised q-dimensions of measures supported by almost self-affine sets, for all q>1. These q-dimensions may exhibit phase transitions as q varies. We first consider general measures and then…

Let $G$ be a cyclic $p$-group or generalized quaternion group, $X\in \pi_0 S_G$ be a virtual $G$-set, and $V$ be a fixed point free complex $G$-representation. Under conditions depending on the sizes of $G$, $X$, and $V$, we construct a…