Cup products and finite loop spaces

Finite loop spaces are manifolds

One of the motivating questions for surgery theory was whether every finite H:space is homotopy equivalent to a Lie group. This question was answered in the negative by Hilton and Roitberg 's discovery of some counterexamples [18]. However, the problem remained whether every finite H-space is homotopy equivalent to a closed, smooth manifold. This question is still open, but in case the H-space ...

Unitary embeddings of finite loop spaces

In this paper we construct faithful representations of saturated fusion systems over discrete p-toral groups and use them to find conditions that guarantee the existence of unitary embeddings of p-local compact groups. These conditions hold for the ClarkEwing and Aguadé-Zabrodsky p-compact groups as well as some exotic 3-local compact groups. We also show the existence of unitary embeddings of ...

Connected Finite Loop Spaces with Maximal Tori

Finite loop spaces are a generalization of compact Lie groups. However, they do not enjoy all of the nice properties of compact Lie groups. For example, having a maximal torus is a quite distinguished property. Actually, an old conjecture, due to Wilkerson, says that every connected finite loop space with a maximal torus is equivalent to a compact connected Lie group. We give some more evidence...

Countable Products of Spaces of Finite Sets

σn(Γ) = {x ∈ {0, 1} Γ : |supp(x)| ≤ n}. Here supp(x) = {γ ∈ Γ : xγ 6= 0}. This is a closed, hence compact subset of {0, 1}, which is identified with the family of all subsets of Γ of cardinality at most n. In this work we will study the spaces which are countable products of spaces σn(Γ), mainly their topological classification as well as the classification of their Banach spaces of continuous ...

Note on Cup-products