Degeneracies in quasi-categories

In this note we show that a semisimplicial set with the weak Kan condition admits a simplicial structure, provided any object allows an idempotent self-equivalence. Moreover, any two choices of simplicial structures give rise to equivalent quasi-categories. The method is purely combinatorial and extends to semisimplicial objects in other categories; in particular to semi-simplicial spaces satisfying the Segal condition (semi-Segal spaces).Comment: 10 pages; minor correction

Higher Whitehead torsion and the geometric assembly map

We construct a higher Whitehead torsion map, using algebraic K-theory of spaces, and show that it satisfies the usual properties of the classical Whitehead torsion. This is used to describe a "geometric assembly map" defined on stabilized structure spaces in purely homotopy theoretic terms.Comment: 46 pages. Revised version following the referee's suggestions. To appear in Journal of Topolog

Stage-worlds and world-stages in Hollywood musicals

Hollywood musicals combine two distinctive features: narrative and musical numbers, also referred to as “the real and the expressive” (Telotte 1980a, 4). These two equally important parts of any successful musical have to harmonize such that both seem appropriate in each scene and, ideally, supportive of each other. As musical numbers are traditionally seen as a “source of a tension” (ibid., 2) within the narrative, harmonization is not easy to achieve, and different directors as well as different sub-genres of the film musical have found different ways to deal with this tension. In this work, I will discuss two methods of integrating musical numbers into the plot of Hollywood musicals: the stage-worlds and the world-stages. While the former entails a certain kind of storyline, the latter refers to the setting of single numbers within the plot

Benthic macrofauna and habitat monitoring on the Continental Shelf of the northeastern United States: I. Biomass

Information on long-term temporal variability of and trends in benthic community-structure variables, such as biomass, is needed to estimate the range of normal variability in comparison with the effects of environmental change or disturbance. Fishery resource distribution and population growth will be influenced by such variability. This study examines benthic macrofaunal biomass and related data collected annually between 1978 and 1985 at 27 sites on the continental shelf of the northwestern Atlantic, from North Carolina to the southern Gulf of Maine. The study was expanded at several sites with data from other studies collected at the same sites prior to 1978. Results indicate that although there was interannual and seasonal variability, as expected, biomass levels over the study period showed few clear trends. Sites exhibiting trends were either in pollution-stressed coastal areas or influenced by the population dynamics of one or a few species, especially echinoderms. (PDF file contains 34 pages.

Parametrized cobordism categories and the Dwyer-Weiss-Williams index theorem

We define parametrized cobordism categories and study their formal properties as bivariant theories. Bivariant transformations to a strongly excisive bivariant theory give rise to characteristic classes of smooth bundles with strong additivity properties. In the case of cobordisms between manifolds with boundary, we prove that such a bivariant transformation is uniquely determined by its value at the universal disk bundle. This description of bivariant transformations yields a short proof of the Dwyer-Weiss-Williams family index theorem for the parametrized A-theory Euler characteristic of a smooth bundle.Comment: 22 pages; minor changes; to appear in the Journal of Topolog

On the hh-cobordism category. I

We consider the topological category of $h$-cobordisms between manifolds with boundary and compare its homotopy type with the standard $h$-cobordism space of a compact smooth manifold.Comment: 23 pages; simplified argument in section 5 and other minor revisions. Final version, to appear in Int. Math. Res. No

Reef Habitats in the Middle Atlantic Bight: Abundance, Distribution, Associated Biological Communities, and Fishery Resource Use

One particular habitat type in the Middle Atlantic Bight is not well recognized among fishery scientists and managers, although it is will known and used by recreational and commercial fisheries. This habitat consists of a variety of hard-surface, elevated relief "reef" or reef-like environments that are widely distributed across the predominantly flat or undulating, sandy areas of the Bight and include both natural rocky areas and man-made structures, e.g. shipwrecks and artificial reefs. Although there are natural rock and shellfish reefs in southern New England coastal waters and estuaries throughout the Bight, most reef habitats in the region appear to be man-made reef habitat modification/creation may be increasing. Very little effort has been devoted to the study of this habitat's distribution, abundance, use by living marine resources and associated biological communities (except on estuarine oyster reefs) and fishery value or management. This poorly studied and surveyed habitat can provide fish refuge from trawls and can be a factor in studies of the distribution and abundance of a variety of reef-associated fishery resources. This review provides a preliminary summary of information found on relative distribution and abundance of reef habitat in the Bight, the living marine resources and biological communities that commonly use it, threats to this habitat and its biological resources, and the value or potential value of artificial reefs to fishery or habitat and its biological resources, and the value or potential value of artificial reefs to fishery or habitat managers. The purpose of the review is to initiate an awareness among resource managers about this habitat, its role in resource management, and the need for research

The space of metrics of positive scalar curvature

We study the topology of the space of positive scalar curvature metrics on high dimensional spheres and other spin manifolds. Our main result provides elements of infinite order in higher homotopy and homology groups of these spaces, which, in contrast to previous approaches, are of infinite order and survive in the (observer) moduli space of such metrics. Along the way we construct smooth fiber bundles over spheres whose total spaces have non-vanishing A-hat-genera, thus establishing the non-multiplicativity of the A-hat-genus in fibre bundles with simply connected base.Comment: 24 pages, v2: minor additions and corrections, based in particular on comments of referees, v3: minor corrections, final version, to appear in Publ.Math. IHE