Generating the Johnson filtration

For k >= 1, let Torelli_g^1(k) be the k-th term in the Johnson filtration of the mapping class group of a genus g surface with one boundary component. We prove that for all k, there exists some G_k >= 0 such that Torelli_g^1(k) is generated by elements which are supported on subsurfaces whose genus is at most G_k. We also prove similar theorems for the Johnson filtration of Aut(F_n) and for certain mod-p analogues of the Johnson filtrations of both the mapping class group and of Aut(F_n). The main tools used in the proofs are the related theories of FI-modules (due to the first author together with Ellenberg and Farb) and central stability (due to the second author), both of which concern the representation theory of the symmetric groups over Z.Comment: 32 pages; v2: paper reorganized. Final version, to appear in Geometry and Topolog

On finite generation of the Johnson filtrations

We prove that every term of the lower central series and Johnson filtrations of the Torelli subgroups of the mapping class group and the automorphism group of a free group is finitely generated in a linear stable range. This was originally proved for the second terms by Ershov and He.Comment: 32 pages. v2: very minor edits. Weaker versions of the results of this paper previously appeared in arXiv:1704.01529 and arXiv:1703.04190v

Integrality in the Steinberg module and the top-dimensional cohomology of SL_n(O_K)

We prove a new structural result for the spherical Tits building attached to SL_n(K) for many number fields K, and more generally for the fraction fields of many Dedekind domains O: the Steinberg module St_n(K) is generated by integral apartments if and only if the ideal class group cl(O) is trivial. We deduce this integrality by proving that the complex of partial bases of O^n is Cohen-Macaulay. We apply this to prove new vanishing and nonvanishing results for H^{vcd}(SL_n(O_K); Q), where O_K is the ring of integers in a number field and vcd is the virtual cohomological dimension of SL_n(O_K). The (non)vanishing depends on the (non)triviality of the class group of O_K. We also obtain a vanishing theorem for the cohomology H^{vcd}(SL_n(O_K); V) with twisted coefficients V.Comment: 36 pages; final version; to appear in Amer. J. Mat

A stability conjecture for the unstable cohomology of SL_n Z, mapping class groups, and Aut(F_n)

In this paper we conjecture the stability and vanishing of a large piece of the unstable rational cohomology of SL_n Z, of mapping class groups, and of Aut(F_n).Comment: 18 pages. v2: final version, to appear in Algebraic Topology: Applications and New Directions, AMS Contemporary Mathematics Serie

Cohesion, competition and contradiction : INTERREG and Franco-British Cross border co-operation

Aquest article resumeix el desenvolupament del programa INTERREG i la cooperació a la frontera franc-britànica en els últims vint anys. Això és seguit per una anàlisi de la forma transfronterera cooperació pot entendre recorrent a les discussions conceptuals de canviar la governança europea i les relacions de poder entre els diferents nivells de govern. Aquestes idees conceptuals proporcionen un context per a un examen en profunditat de la iniciativa INTERREG IIIA, a la frontera franc-britànica que es destaquen alguns dels principals problemes i les contradiccions de la cooperació transfronterera.This paper summarise the development of the INTERREG programme and co-operation on the Franco-British border over the last twenty years. This is followed by a consideration of how cross-border co-operation can be understood by drawing on conceptual discussions of changing European governance and the power relations between different tiers of government. These conceptual ideas provide a context for an in depth consideration of the INTERREG IIIA initiative on the Franco-British border which highlights some of the key problems and contradictions of cross border co-operation

The economic regeneration of London docklands: a labour market analysis

PhDIn 1980 the London Docklands Development Corporation (LDDC) was designated as the organisation responsible for the physical, economic and social regeneration of the area in East London known as London Docklands. It-is argued that an evaluation of LDDC policy impact on the labour market will be useful for two reasons. First, it will make a contribution to the academic discussion on the causes of economic and social change in this part of London. This is made all the more necessary because much previous research has concentrated on political issues, whilst paying only lip-service to many of the other economic and social forces that cause change. Second, at a practical level, the controversial nature of LDDC initiatives necessitates a detailed study of policy impact. A conceptual model of the labour market is developed based on segmented labour market theory. It includes the key influences on the demand and supply side of the labour market and the interaction process between demand and supply. This allows the evaluation of LDDC policy to take account of other forces that cause change in the labour market. The broad conclusion is that LDDC policy has had a very limited impact on the local labour market and an explanation of change in London Docklands must include other economic and social forces

The Knowledge of the Heart: Reading the Ancrene Wisse in the Context of Twelfth-Century Monastic Conscience Literature

This thesis addresses the nature and role of contemplation in the early-thirteenth-century English Ancrene Wisse (AW). Previous scholarship on the text has debated whether or not it ought to be described as ‘mystical,’ and has generally focused on language and imagery that the AW shares with more conventionally recognised mystical literature. This thesis takes a different approach by focusing on the role of the conscience within the text. The AW prescribes a rule of life that governs the heart. The AW author defines a pure heart as a clean conscience. An attempt to understand the contemplative life in the AW must first establish what the author means by the conscience; applications of modern and medieval scholastic understandings of the conscience to the AW are anachronistic. This thesis explores the AW author’s handling of conscience within the context of twelfth-century monastic thought, as expressed in three treatises on conscience which have hitherto received minimal scholarly attention: Peter of Celle’s De Conscientia, and the pseudo-Bernardine Tractatus de Conscientia and De Interiori Domo. In these texts, conscience is neither a moral guide nor a record of personal conduct. Their authors synthesise a new understanding of the conscience from different elements within classical, biblical, and patristic thought. This thesis argues that this distinctive approach to conscience gave rise to a different form of contemplative thought and practice that lies outside the mainstream development of medieval mysticism. Rather than utilising tripartite schemas of spiritual ascent based on the stages of purgation, illumination, and union, the conscience texts base their view of union with God on the model of moral reasoning. This thesis argues that the AW participates in this school of thought on conscience and contemplation, rather than more conventionally recognised traditions of medieval mystical literature

The progenitors of calcium-rich transients are not formed in situ

We present deep VLT and HST observations of the nearest examples of calcium-rich 'gap' transients -- rapidly evolving transient events, with a luminosity intermediate between novae and supernovae. These sources are frequently found at large galactocentric offsets, and their progenitors remain mysterious. Our observations find no convincing underlying quiescent sources coincident with the locations of these transients, allowing us to rule out a number of potential progenitor systems. The presence of surviving massive-star binary companions (or other cluster members) are ruled out, providing an independent rejection of a massive star origin for these events. Dwarf satellite galaxies are disfavoured unless one invokes as yet unknown conditions that would be extremely favourable for their production in the lowest mass systems. Our limits also probe the majority of the globular cluster luminosity function, ruling out the presence of an underlying globular cluster population at high significance, and thus the possibility that they are created via dynamical interactions in dense globular cluster cores. Given the lack of underlying systems, previous progenitor suggestions have difficulty reproducing the remote locations of these transients, even when considering solely halo-borne progenitors. Our preferred scenario is that calcium-rich transients are high velocity, kicked systems, exploding at large distances from their natal site. Coupled with a long-lived progenitor system post-kick, this naturally explains the lack of association these transients have with their host stellar light, and the extreme host-offsets exhibited. Neutron star -- white dwarf mergers may be a promising progenitor system in this scenario.Comment: Accepted for publication in MNRAS, 11 pages, 9 figure