Showing papers in "Mathematica Scandinavica in 1990"

4-critical 4-valent planar graphs constructed with crowns.

Abstract: A construction of arbitrarily large 4-critical 4-valent planar graphs with aid of socalled «crowns» is given which also proves a conjecture of B. Grunbaum. Furthermore some coloring properties of the aid graphs are derived

Leading terms in the heat invariants for the Laplacians of the De Rham signature, and spin complexes.

Abstract: Let D be a vector bundle-valued differential operator with positive definite leading symbol on a compact, Riemannian manifold Asymptotic expansions of the kernel function and L 2 trace of the heat operator e -tD , t>0, naturally lead to sequences of homogeneous local and global scalar invariants a n (x,D), a n (D)≡⇇∫a n (x,D), n∈N Within each homogeneity class of local invariants, there is a filtration by degree; the lowest-degree terms in a n (x,D) are linear, those in a n (D) quadratic We specialize our earlier general results to give such leading terms in the heat invariants produced by the Laplacians of the de Rham, signature, and spin complexes A main technical point is a calculation of fiber traces of quadratic expressions built form iterated covariant derivatives of the Weitzenbock operator