Topological Hochschild homology of Thom spectra and the free loop space

We describe the topological Hochschild homology of ring spectra that arise as Thom spectra for loop maps f: X->BF, where BF denotes the classifying space for stable spherical fibrations. To do this, we consider symmetric monoidal models of the category of spaces over BF and corresponding strong symmetric monoidal Thom spectrum functors. Our main result identifies the topological Hochschild homology as the Thom spectrum of a certain stable bundle over the free loop space L(BX). This leads to explicit calculations of the topological Hochschild homology for a large class of ring spectra, including all of the classical cobordism spectra MO, MSO, MU, etc., and the Eilenberg-Mac Lane spectra HZ/p and HZ.Comment: 58 page

Homology and Derived Series of Groups II: Dwyer's Theorem

We give new information about the relationship between the low-dimensional homology of a group and its derived series. This yields information about how the low-dimensional homology of a topological space constrains its fundamental group. Applications are given to detecting when a set of elements of a group generates a subgroup ``large enough'' to map onto a non-abelian free solvable group, and to concordance and grope cobordism of links. We also greatly generalize several key homological results employed in recent work of Cochran-Orr-Teichner, in the context of classical knot concordance. In 1963 J. Stallings established a strong relationship between the low-dimensional homology of a group and its lower central series quotients. In 1975 W. Dwyer extended Stallings' theorem by weakening the hypothesis on the second homology groups. The naive analogues of these theorems for the derived series are false. In 2003 the second author introduced a new characteristic series, associated to the derived series, called the torsion-free derived series. The authors previously established a precise analogue, for the torsion-free derived series, of Stallings' theorem. Here our main result is the analogue of Dwyer's theorem for the torsion-free derived series. We also prove a version of Dwyer's theorem for the rational lower central series. We apply these to give new results on the Cochran-Orr-Teichner filtration of the classical link concordance group.Comment: 26 pages. In this version, we have included a new proof of part of the main theorem. The new proof is somewhat simpler and stays entirely in the world of group homology and homological algebra rather than using Eilenberg-Mac Lane spaces. Other minor corrections. This is the final version to appear in Geometry & Topolog

The de Rham homotopy theory and differential graded category

This paper is a generalization of arXiv:0810.0808. We develop the de Rham homotopy theory of not necessarily nilpotent spaces, using closed dg-categories and equivariant dg-algebras. We see these two algebraic objects correspond in a certain way. We prove an equivalence between the homotopy category of schematic homotopy types and a homotopy category of closed dg-categories. We give a description of homotopy invariants of spaces in terms of minimal models. The minimal model in this context behaves much like the Sullivan's minimal model. We also provide some examples. We prove an equivalence between fiberwise rationalizations and closed dg-categories with subsidiary data.Comment: 47 pages. final version. The final publication is available at http://www.springerlink.co

"It All Ended in an Unsporting Way": Serbian Football and the Disintegration of Yugoslavia, 1989-2006

Part of a wider examination into football during the collapse of Eastern European Communism between 1989 and 1991, this article studies the interplay between Serbian football and politics during the period of Yugoslavia's demise. Research utilizing interviews with individuals directly involved in the Serbian game, in conjunction with contemporary Yugoslav media sources, indicates that football played an important proactive role in the revival of Serbian nationalism. At the same time the Yugoslav conflict, twinned with a complex transition to a market economy, had disastrous consequences for football throughout the territories of the former Yugoslavia. In the years following the hostilities the Serbian game has suffered decline, major financial hardship and continuing terrace violence, resulting in widespread nostalgia for the pre-conflict era

BV-structures on the homology of the framed long knot space

We introduce BV-algebra structures on the homology of the space of framed long knots in $\mathbb{R}^n$ in two ways. The first one is given in a similar fashion to Chas-Sullivan's string topology. The second one is defined on the Hochschild homology associated with a cyclic, multiplicative operad of graded modules. The latter can be applied to Bousfield-Salvatore spectral sequence converging to the homology of the space of framed long knots. Conjecturally these two structures coincide with each other.Comment: 13 pages, 3 figures, to appear in Journal of Homotopy and Related Structure

On the Whitehead spectrum of the circle

The seminal work of Waldhausen, Farrell and Jones, Igusa, and Weiss and Williams shows that the homotopy groups in low degrees of the space of homeomorphisms of a closed Riemannian manifold of negative sectional curvature can be expressed as a functor of the fundamental group of the manifold. To determine this functor, however, it remains to determine the homotopy groups of the topological Whitehead spectrum of the circle. The cyclotomic trace of B okstedt, Hsiang, and Madsen and a theorem of Dundas, in turn, lead to an expression for these homotopy groups in terms of the equivariant homotopy groups of the homotopy fiber of the map from the topological Hochschild T-spectrum of the sphere spectrum to that of the ring of integers induced by the Hurewicz map. We evaluate the latter homotopy groups, and hence, the homotopy groups of the topological Whitehead spectrum of the circle in low degrees. The result extends earlier work by Anderson and Hsiang and by Igusa and complements recent work by Grunewald, Klein, and Macko.Comment: 52 page

La vie et la mort en peinture

L'abstraction visuelle ne constituerait pas d'abord une réflexion sur la nature du beau en soi, mais une approche cognitive renvoyant aux épistémologies et aux idéologies des époques où elle se manifeste. L'étude de différents discours tenus sur l'abstraction picturale au XIXe et au XXe siècles permet de suivre les valeurs attribuées à cette notion, notamment autour de l'opposition entre le vitalisme et la mort à partir des réflexions d'A. Riegl et W. Worringer. La différenciation entre l'abstrait et le concret, le sujet et l'objet se voit ainsi constamment relancée, dans la possibilité de leur réversibilité.Visual abstraction is not, at least not in the first place, a reflection upon the nature of beauty as such, but rather a cognitive approach to the world that bears witness to the epistemologies and ideologies of those periods of history where it appeared. The study of some of the discourses that have been held about pictural abstraction during the 19th and 20th centuries, notably the opposition between vitalism and death founded on the works of A. Riegl and W. Worringer, allows us to understand the various values that have been given to the notion. The distinction between abstraction and concreteness, subject and object, can here be seen, in regard to the possibility of their reversibility, as an ever-open question

Exploring children’s perspectives on the welfare needs of pet animals

This work was supported by the Department for Environment, Food and Rural Affairs (grant number AW1404).Children are increasingly viewed as important recipients of eduational interventions to improve animal welfare, yet research examining their perspectives is lacking, particularly within the UK. Helping children to care appropriately for animals depends, not least, on an ability to understand the needs of different species and correctly identify cues given by the animal that indicate its welfare state. This study began to explore: (a) children’s perceptions of welfare needs, focusing on four common pet animals; (b) influences on the development of knowledge; (c) beliefs about whether or not (all) animals are sentient, and (d) their confidence in identifying when their own pets are in need. Fourteen focus groups were carried out with 53 children aged 7 to 13 years. Findings highlighted an affirmative response that animals have feelings (dogs especially), albeit with doubts about this applying universally. There was wide variation in children’s knowledge of welfare needs, even among owners of the animal in question. Conversely, some children lacked confidence in spite of the extensive knowledge they had developed through direct experience. An important finding was a perceived difficulty in identifying the needs of particular species or specific types of need in their own pets. Fitting well with a recent emphasis on “positive welfare,” children felt that many animals need demonstrative love and attention, especially cats and dogs. While there is clearly scope for educating children about common needs and cues that indicate animals’ welfare state, other areas pose a greater challenge. Emotional connection seems important in the development of extensive knowledge and concern for welfare. Accordingly, animals that do not possess the kind of behavioral repertoire that is easy to interpret or allows for a perceived sense of reciprocity are possibly at risk of negative welfare experiences.PostprintPeer reviewe