The classification of 2-compact groups

We prove that any connected 2-compact group is classified by its 2-adic root datum, and in particular the exotic 2-compact group DI(4), constructed by Dwyer-Wilkerson, is the only simple 2-compact group not arising as the 2-completion of a compact connected Lie group. Combined with our earlier work with Moeller and Viruel for p odd, this establishes the full classification of p-compact groups, stating that, up to isomorphism, there is a one-to-one correspondence between connected p-compact groups and root data over the p-adic integers. As a consequence we prove the maximal torus conjecture, giving a one-to-one correspondence between compact Lie groups and finite loop spaces admitting a maximal torus. Our proof is a general induction on the dimension of the group, which works for all primes. It refines the Andersen-Grodal-Moeller-Viruel methods to incorporate the theory of root data over the p-adic integers, as developed by Dwyer-Wilkerson and the authors, and we show that certain occurring obstructions vanish, by relating them to obstruction groups calculated by Jackowski-McClure-Oliver in the early 1990s.Comment: 47 page

New collections of p-subgroups and homology decompositions for classifying spaces of finite groups

Let G be a finite group and p a prime dividing its order. We define new collections of p-subgroups of G. We study the homotopy relations among them and with the standard collections of p-subgroups. We determine their ampleness and sharpness properties.Comment: 14 pages, some revisions made, final version to appear in Communications in Algebr

Advances and challenges in innovation studies

The article discusses recent advances and future challenges in innovation studies. First, it separately considers four main strands of research, studying innovation at the organizational, systemic, sectoral and macroeconomic levels. Then, considering the field as a whole, the article points to the existence of important neglected topics and methodological challenges for future research. In fact, several fundamental issues are still unexplored, such as the co-evolution between technological and institutional change; the role of demand; and the impacts of innovation on individual and collective welfare. There are also important methodological challenges, such as the need for more systematic interactions between the different levels of analysis; the importance of an interdisciplinary approach to the study of technological and institutional changes; and the search for a combination of contingent explanations based on case studies with general analytical results based on econometric and formal models

Automorphisms of p-compact groups and their root data

We construct a model for the space of automorphisms of a connected p-compact group in terms of the space of automorphisms of its maximal torus normalizer and its root datum. As a consequence we show that any homomorphism to the outer automorphism group of a p-compact group can be lifted to a group action, analogous to a classical theorem of de Siebenthal for compact Lie groups. The model of this paper is used in a crucial way in our paper ``The classification of 2-compact groups'', where we prove the conjectured classification of 2-compact groups and determine their automorphism spaces.Comment: 24 pages. Introduction restructured and title changed (from "Automorphisms of root data, maximal torus normalizers, and p-compact groups"). Various other adjustments mad

A finite loop space not rationally equivalent to a compact Lie group

We construct a connected finite loop space of rank 66 and dimension 1254 whose rational cohomology is not isomorphic as a graded vector space to the rational cohomology of any compact Lie group, hence providing a counterexample to a classical conjecture. Aided by machine calculation we verify that our counterexample is minimal, i.e., that any finite loop space of rank less than 66 is in fact rationally equivalent to a compact Lie group, extending the classical known bound of 5.Comment: 8 page

The Steenrod problem of realizing polynomial cohomology rings

In this paper we completely classify which graded polynomial R-algebras in finitely many even degree variables can occur as the singular cohomology of a space with coefficients in R, a 1960 question of N. E. Steenrod, for a commutative ring R satisfying mild conditions. In the fundamental case R = Z, our result states that the only polynomial cohomology rings over Z which can occur, are tensor products of copies of H^*(CP^\infty;Z) = Z[x_2], H^*(BSU(n);Z) = Z[x_4,x_6,...,x_{2n}], and H^*(BSp(n):Z) = Z[x_4,x_8,...,x_{4n}] confirming an old conjecture. Our classification extends Notbohm's solution for R = F_p, p odd. Odd degree generators, excluded above, only occur if R is an F_2-algebra and in that case the recent classification of 2-compact groups by the authors can be used instead of the present paper. Our proofs are short and rely on the general theory of p-compact groups, but not on classification results for these.Comment: 14 pages. v3: Final version. To appear in Journal of Topolog

Constructing a Distant Future: Imaginaries in Geoengineering

We develop the concept of the distant future as a new way of seeing the future in collective efforts. While a near future is represented in practical terms and concerned with forming expectations and goals under conditions of uncertainty, a distant future is represented in stylized terms and concerned with imagining possibilities under conditions of ambiguity. Management research on future-oriented action has developed around problems of the near future. To explore distant futures, we analyze the case of geoengineering, a set of planetary-scale technologies that have been proposed as solutions to the threat of climate change. Geoengineering has increasingly been treated as if it were a reality, despite continued controversy and in the absence of any implementation. We find that societal-level imaginaries that were built on deeply-held moral bases and cosmologies underpinned the conception of geoengineering, and that a dialectic process of discursive attempts to reconcile oppositional imaginaries increased the concreteness and credibility of geoengineering so that it increasingly has been treated as an ‘as-if’ reality. We suggest that distant futures orient collective efforts in distinctive ways, not as concrete guides for action but by expressing critiques and alternatives, that can become treated as ‘as-if’ realities