In this paper, I construct noncompact analogs of the Chern classes of equivariant vector bundles over complex reductive groups. Then “Chern classes” of the tangent bundle are used to carry over to the case of an arbitrary reductive group some of the well-known results that hold for a complex torus. One of the results of this paper is a formula for the Chern classes of all regular equivariant co...

Generating functions for the number of commuting m-tuples in the symmetric groups are obtained. We define a natural sequence of “orbifold Euler characteristics” for a finite group G acting on a manifold X . Our definition generalizes the ordinary Euler characteristic of X/G and the string-theoretic orbifold Euler characteristic. Our formulae for commuting m-tuples underlie formulas that general...

Dimension is a fundamental concept in topology. Mylopoulos and Pavlidis [17] provided a definition for discrete spaces. In the present paper we propose an alternative one for the case of planar digital objects. It makes up certain shortcomings of the definition from [17] and implies dimensionality properties analogous to those familiar from classical topology. We also establish relations betwee...

We show that the discretized configuration space of k points in the n-simplex is homotopy equivalent to a wedge of spheres of dimension n− k+1. This space is homeomorphic to the order complex of the poset of ordered partial partitions of {1, . . . , n+1} with exactly k parts. We also compute the Euler characteristic in two different ways, thereby obtaining a topological proof of a combinatorial...

The solutions we present have infinite kinetic energy and blow up in finite time. Blow up of other similar infinite energy solutions of Euler equations has been proved before ([1], [2]). The particular type of solution we will describe was proposed in ([3]). The Eulerian-Lagrangian approach we take ([4]) is not restricted to this particular case, but exact integration of the equations is. We wi...

We define the notion of Euler characteristic for definable quotients in an arbitrary o-minimal structure and prove some fundamental properties.

We give lower bounds, in terms of the Euler characteristic, for the L-norm of the Weyl curvature of closed Riemannian 4-manifolds. The same bounds were obtained by Gursky, in the case of positive scalar curvature metrics.

In [2], a {5, 5}-equivelar polyhedral map of Euler characteristic −8 was constructed. In this article we prove that {5, 5}-equivelar polyhedral map of Euler characteristic −8 is unique. As a consequence, we get that the minimum number of edges in a non-orientable polyhedral map of Euler characteristic −8 is > 40. We have also constructed {5, 5}-equivelar polyhedral map of Euler characteristic −...

One special subalgebra of the algebra of fuzzy truth values is the set of those elements that take only 0 and 1 as values. This subalgebra is in one-to-one correspondence with the subsets of the unit interval, but the operations do not correspond to ordinary union and intersection. The automorphisms of this subalgebra are studied here, resulting in showing that the subobjects corresponding to n...

It is a well-known fact that every Riemann surface with negative Euler characteristic admits a hyperbolic metric. But this metric is by no means unique – indeed, there are uncountably many such metrics. In this paper, we study the space of all such hyperbolic structures on a Riemann surface, called the Teichmüller space of the surface. We will show that it is a complete metric space, and that i...