Gross-Hopkins duality

We give a new and simpler proof of a result of Hopkins and Gross relating Brown-Comenetz duality to Spanier-Whitehead duality in the K(n)-local stable homotopy category

K(n)-local duality for finite groups and groupoids

We define an inner product (suitably interpreted) on the K(n)-local spectrum LG := L_{K(n)}BG_+, where G is a finite group or groupoid. This gives an inner product on E^*BG_+ for suitable K(n)-local ring spectra E. We relate this to the usual inner product on the representation ring when n=1, and to the Hopkins-Kuhn-Ravenel generalised character theory. We show that LG is a Frobenius algebra object in the K(n)-local stable category, and we recall the connection between Frobenius algebras and topological quantum field theories to help analyse this structure. In many places we find it convenient to use groupoids rather than groups, and to assist with this we include a detailed treatment of the homotopy theory of groupoids. We also explain some striking formal similarities between our duality and Atiyah-Poincare duality for manifolds.Comment: 37 pages; one included postscript figur

Morava E-theory of symmetric groups

We compute the completed E(n) cohomology of the classifying spaces of the symmetric groups, and relate the answer to the theory of finite subgroups of formal groups.Comment: To appear in Topolog

The Hopf Rings for KO and KU

We compute the mod two homology Hopf rings of the spectra KO and KU. The spaces in these spectra are the infinite classical groups and their coset spaces, and their homology was first calculated in the Cartan seminars, but the Hopf ring structure was first determined in the second author's unpublished PhD thesis. The presentation given here serves as an introduction to the first author's much more intricate work on the connective spectrum bo. The Hopf ring viewpoint turns out to be very convenient for understanding the homological effect of various maps between classical groups and fibrations of their connective covers.Comment: 20 pages; to appear in JPA

Phantom Maps and Homology Theories

We study phantom maps and homology theories in a stable homotopy category S via a certain Abelian category A. We express the group P(X,Y) of phantom maps X -> Y as an Ext group in A, and give conditions on X or Y which guarantee that it vanishes. We also determine P(X,HB). We show that any composite of two phantom maps is zero, and use this to reduce Margolis's axiomatisation conjecture to an extension problem. We show that a certain functor S -> A is the universal example of a homology theory with values in an AB 5 category and compare this with some results of Freyd.Comment: 25 pages, AMSLaTeX, to appear in Topolog

Indicated prevention interventions for anxiety in children and adolescents: a review and meta-analysis of school-based programs

Anxiety disorders are among the most common youth mental health disorders. Early intervention can reduce elevated anxiety symptoms. School-based interventions exist but it is unclear how effective targeted approaches are for reducing symptoms of anxiety. This review and meta-analysis aimed to determine the effectiveness of school-based indicated interventions for symptomatic children and adolescents. The study was registered with PROSPERO [CRD42018087628]. We searched MEDLINE, EMBASE, PsycINFO, and the Cochrane Library for randomised-controlled trials comparing indicated programs for child and adolescent (5–18 years) anxiety to active or inactive control groups. Data were extracted from papers up to December 2019. The primary outcome was efficacy (mean change in anxiety symptom scores). Sub-group and sensitivity analyses explored intervention intensity and control type. We identified 20 studies with 2076 participants. Eighteen studies were suitable for meta-analysis. A small positive effect was found for indicated programs compared to controls on self-reported anxiety symptoms at post-test (g = − 0.28, CI = − 0.50, − 0.05, k = 18). This benefit was maintained at 6 (g = − 0.35, CI = − 0.58, − 0.13, k = 9) and 12 months (g = − 0.24, CI = − 0.48, 0.00, k = 4). Based on two studies, > 12 month effects were very small (g = − 0.01, CI = − 0.38, 0.36). No differences were found based on intervention intensity or control type. Risk of bias and variability between studies was high (I2 = 78%). Findings show that school-based indicated programs for child and adolescent anxiety can produce small beneficial effects, enduring for up to 12 months. Future studies should include long-term diagnostic assessments

Productive resistance within the public sector: exploring organisational culture

The article examines how South Korean civil servants responded to the introduction of pay for performance. Drawing upon 31 in-depth interviews with career civil servants, it identifies what became known as 1/n, a form of ‘discreet resistance’ that emerged and evolved. The analytical framework allows productive resistance to be seen as ebbing and flowing during organisational change that sees institutionalisation, deinstitutionalisation and re-institutionalisation. In understanding the cultural context of organisational resistance the contribution is three-fold. First, a nuanced definition and understanding of productive resistance. Second, it argues that productive resistance must be seen as part of a process that does not simply reflect ‘offer and counter-offer’ within the change management process. Thirdly, it identifies differences within groups and sub-cultures concerning commitment towards resistance and how these fissures contribute towards change as new interpretive schemes and justifications are presented in light of policy reformulations