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Morita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity
Andrés Angel, Hellen Colman, Mark Grant +1
We use the homotopy invariance of equivariant principal bundles to prove that the equivariant -category of Clapp and Puppe is invariant under Morita equivalence. As a…
A Motion Planning Algorithm in a lollipop graph
Allaoua Boughrira, Hellen Colman
This paper is concerned with problems relevant to motion planning in robotics. Configuration spaces are of practical relevance in designing safe control schemes for robots moving o…
Equivariant topological complexities
Andres Angel, Hellen Colman
The aim of this article is to review different generalizations of the the notion of topological complexity to the equivariant setting. In particular, we review the relation (or non…
The Lusternik-Schnirelmann category of a Lie groupoid
Hellen Colman
We propose a new homotopy invariant for Lie groupoids which generalizes the classical Lusternik-Schnirelmann category for topological spaces. We use a bicategorical approach to dev…
On the 1-homotopy type of Lie groupoids
Hellen Colman
We propose a notion of 1-homotopy for generalized maps. This notion generalizes those of natural transformation and ordinary homotopy for functors. The 1-homotopy type of a Lie gro…