Automorphisms compatible with group actions

Group Actions, Coverings and Lifts of Automorphisms Group Actions, Coverings and Lifts of Automorphisms

a Supported in part by \Ministrstvo za znanost in tehnologijo Slovenije", proj.no. Abstract The problem of lifting automorphisms of a (fairly arbitrary) topological space to automorphisms of a covering space is studied by means of voltage groups. To this end we introduce some required background results regarding group actions and covering spaces.

Complexes with free actions by the group of automorphisms of a free group

We define two finite-dimensional complexes on which the group Aut(Fn) acts freely, and study their homotopy groups. The definitions of these complexes were motivated by lowdimensional pseudo-isotopy theory. So not surprisingly, the complexes are related to a number of spaces arising in algebraic K-theory, and to another in low-dimensional topology. The complexes are denoted by Xn and X alg n . ...

Actions and Automorphisms of Crossed Modules

Faithful actions of automorphisms on the space of orderings of a group

In this article we study the space of leftand bi-invariant orderings on a torsion-free nilpotent group G. We will show that generally the set of such orderings is equipped with a faithful action of the automorphism group of G. We prove a result which allows us to establish the same conclusion when G is assumed to be merely residually torsion-free nilpotent. In particular, we obtain faithful act...

Group Discounts Compatible with Buyer Privacy

We show how group discounts can be offered without forcing buyers to surrender their anonymity, as long as buyers can use their own computing devices (e.g. smartphone, tablet or computer) to perform a purchase. Specifically, we present a protocol for privacy-preserving group discounts. The protocol allows a group of buyers to prove how many they are without disclosing their identities. Coupled ...