Remarks on the equivariant degree theory

Some Remarks on Degree Theory for So(2)-equivariant Transversal Maps

The aim of this article is to introduce a new class SO(2)equivariant transversal maps T R(cl(Ω), ∂Ω) and to define degree theory for such maps. We define degree for SO(2)-equivariant transversal maps and prove some properties of this invariant. Moreover, we characterize SO(2)-equivariant transversal isomorphisms and derive formula for degree of such isomorphisms.

Remarks on Binding Theory

We propose some reformulations of binding principle A that build on recent work by Pollard and Xue, and by Runner et al. We then turn to the thorny issue of the status of indices, in connection with the seemingly simpler Principle B. We conclude that the notion of index is fundamentally incoherent, and suggest some possible approaches to eliminating them as theoretical primitives. One possibili...

Equivariant cohomology and equivariant intersection theory

This text is an introduction to equivariant cohomology, a classical tool for topological transformation groups, and to equivariant intersection theory, a much more recent topic initiated by D. Edidin and W. Graham. It is based on lectures given at Montréal is Summer 1997. Our main aim is to obtain explicit descriptions of cohomology or Chow rings of certain manifolds with group actions which ar...

Remarks on Classical Invariant Theory

A uniform formulation, applying to all classical groups simultaneously, of the First Fundamental Theory of Classical Invariant Theory is given in terms of the Weyl algebra. The formulation also allows skew-symmetric as well as symmetric variables. Examples illustrate the scope of this formulation.

Remarks on Formal Knot Theory