1,002 research outputs found
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-brità nica en els últims vint anys. Això és seguit per una anà lisi 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-brità nica 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
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