Nonlinear Equivariant Automorphisms

An Equivariant Whitehead Algorithm and Conjugacy for Roots of Dehn Twists

§0. Introduction In 1912 Max Dehn formulated fundamental problems concerning a group given by generators and relations. One of these, the conjugacy problem, asks whether there is an algorithm to decide whether two words in the generators represent conjugate elements of the group. Dehn himself gave an elegant solution to this problem in the case when the group is the fundamental group of a close...

Equivariant Polynomial Automorphisms of -representations

We show that every equivariant polynomial automorphism of a-representation and of the reduction of an irreducible-representation is a multiple of the identity.

SL2-equivariant polynomial automorphisms of the binary forms

Equivariant ^-theory for Noetherian Rings

A number of results are proved concerning the Quillen ^-theory K+(S*G) of the skew group ring S*G, where S is a Noetherian ring and G is a finite group of automorphisms of 5. Applications are given to the computation of AT-groups of group algebras and of equivariant /^-theory for affine varieties.

The Tangent Space of the Deformation Functor of Curves with Automorphisms

The dimension of the tangent space to the global infinitesimal deformation functor of a curve together with a subgroup of the group of automorphisms is computed with the aid of equivariant cohomology. The computational techniques we developed are applied to the case of the Fermat curves.