Compact perturbations of Fredholm $n$-tuples

Probability of Mutually Commuting N-Tuples in Some Classes of Compact Groups

probability of mutually commuting n-tuples in some classes of compact groups

Orbits on n-tuples

A transitive (infinite) permutation group which has m orbits on ordered pairs of distinct points has at least mn−1 orbits on ordered n-tuples. This is best possible, and groups attaining the bound can be characterised.

Packing of graphic n-tuples

An n-tuple π (not necessarily monotone) is graphic if there is a simple graph G with vertex set {v1, . . . , vn} in which the degree of vi is the ith entry of π. Graphic n-tuples (d (1) 1 , . . . , d (1) n ) and (d (2) 1 , . . . , d (2) n ) pack if there are edge-disjoint n-vertex graphs G1 and G2 such that dG1(vi) = d (1) i and dG2(vi) = d (2) i for all i. We prove that graphic n-tuples π1 and...

Cohomology of the Space of Commuting N-tuples in a Compact Lie Group

Consider the space Hom(Z n , G) of pairwise commuting n-tuples of elements in a compact Lie group G. This forms a real algebraic variety, which is generally singular. In this paper, we construct a desingulariza-tion of the generic component of Hom(Z n , G), which allows us to derive formulas for its singular and equivariant cohomology in terms of the Lie algebra of a maximal torus in G and the ...