Après un Master consacré aux espaces connectifs à l'Université de Freiburg, P. Turk a rejoint depuis mai 2018 la Fondation pour la recherche scientifique et industrielle (SINTEF) à Oslo.
Abstract: We begin by constructing functors between the category Top and several categories of connective spaces. With certain restrictions, we can use these functors to translate the notion of continuity of maps from topological into connective language.
Given this, we have the necessary tools to define homotopies on connective spaces and construct a connective homotopy theory that is analogous to its topological archetype.
Finally, we discuss how our homotopy theory behaves on graphs (defined as connective spaces). As it turns out, we can even use certain manifolds to construct graphs in such a way, that all of their homotopy groups will be isomorphic.