2026-05-28T16:33:46Zhttps://riuma.uma.es/rest/oai/request

oai:riuma.uma.es:10630/193252026-02-03T12:35:17Zcom_10630_2254col_10630_37957

00925njm 22002777a 4500 dc Mendez Martinez, David author 2020-02-24 Realisability problems in Algebraic Topology are very easy to state and extremely hard to solve. Three classic examples of this are: the realisability of cohomology algebras, proposed by N. E. Steenrod in the 1960s, which asks for a characterisation of graded algebras that appear as the cohomology of a certain space; the problem of Moore G-spaces, also proposed by Steenrod, which asks for the characterisation of ZG-modules that appear as the homology of Moore G-spaces; and the problem of realisability of abstract groups proposed by D. Kahn which asks for the characterisation of groups that appear as the group of self-equivalences of simply connected spaces. These three problems have in common the pursuit of spaces that realise an algebraic structure through an homotopy invariant. In this work we focus on Kahn’s problem, which was introduced in the sixties and received quite a lot of attention, even if progress towards a general solution to it was slow at first. Kahn’s problem is the case C = HoTop of the more general group realisability problem, which asks if every group appears as the automorphism group of an object in a given category C. And it is precisely a classical solution to this more general problem in the category of C = Graphs that led to the most important breakthrough so far with relation to Kahn’s problem: in 2014, Costoya-Viruel showed that every finite group is the group of self-homotopy equivalences of a rational space by building a nice functor from a subcategory of Graphs to the category C = CDGAs, algebraic models of rational homotopy types of spaces. https://hdl.handle.net/10630/19325 Topología algebraica Realisability problems in Algebraic Topology