Partition Complexes, Tits Buildings and Symmetric Products

We construct a homological approximation to the partition complex,and identify it as the Tits building. This gives a homologicalrelationship between the symmetric group and the affine group,leads to a geometric tie between symmetric powers of spheresand the Steinberg idempotent, and allows us to use the self-dualityof the Steinberg module to study layers in the Goodwillie towerof the identity functor. 2000 Mathematics Subject Classification:55N25, 55S15, 20B30, 55P25.     

Calculus of functors,operad formality,and rational homology of embedding spaces

Let M be a smooth manifold and V a Euclidean space. Let [`(\textEmb)] \overline{{{\text{Emb}}}} (M,V) be the homotopy fiber of the map Emb(M,V) → Imm(M,V). This paper is about the rational homology of [`(\textEmb)] \overline{{{\text{Emb}}}} (M,V). We study it by applying embedding calculus and orthogonal calculus to the bifunctor (M,V)↦ HQ ∧ [`(\textEmb)] \overline{{{\text{Emb}}}} (M,V)₊. Our main theorem states that if

Mapping spaces and homology isomorphisms

Let denote the space of pointed continuous maps from a finite cell complex to a space . Let be a generalized homology theory. We use Goodwillie calculus methods to prove that under suitable conditions on and , will send an -isomorphism in either variable to a map that is monic in homology. Interesting examples arise by letting be -theory, the finite complex be a sphere, and the map in the variable be an exotic unstable Adams map between Moore spaces.

     

Monitoring of pesticides in surface water: Off-line SPE followed by HPLC with UV detection and confirmatory analysis by mass spectrometry

Summary The presence of 16 of the most widely used pesticides in southern Italy (plus atrazine, the use of which is currently restricted in Europe) has been monitored in ten surface waters of the Calabria Region. The analytes were extracted from water by off-line solid-phase extraction with a Carbograph cartridge. Base-neutral, and acid pesticides were then isolated by differential elution. Analyte fractionation and quantification were performed by liquid chromatography (HPLC) with UV detection. Recoveries of analytes from 0.5 L river water (200 ngL⁻¹ spike level) were ≥84%. Confirmatory analysis was performed by HPLC coupled with ion-spray mass spectrometry (LC-ESI-MS).     

The action of Young subgroups on the partition complex

Publications mathématiques de l'IHÉS - We study the restrictions, the strict fixed points, and the strict quotients of the partition complex $|\Pi_{n}|$ , which is the $\Sigma_{n}$...     

A generalization of Snaith-type filtration

In this paper we describe the Goodwillie tower of the stable homotopy of a space of maps from a finite-dimensional complex to a highly enough connected space. One way to view it is as a partial generalization of some well-known results on stable splittings of mapping spaces in terms of configuration spaces.

     

A classification of Taylor towers of functors of spaces and spectra

We describe new structure on the Goodwillie derivatives of a functor, and we show how the full Taylor tower of the functor can be recovered from this structure. This new structure takes the form of a coalgebra over a certain comonad which we construct, and whose precise nature depends on the source and target categories of the functor in question. The Taylor tower can be recovered from standard cosimplicial cobar constructions on the coalgebra formed by the derivatives. We get from this an equivalence between the homotopy category of polynomial functors and that of bounded coalgebras over this comonad.     

The Mitchell-Richter filtration of loops on Stiefel manifolds stably splits

We prove that the Mitchell-Richter filtration of the space of loops on complex Stiefel manifolds stably splits. The result is obtained as a special case of a more general splitting theorem. Another special case is H. Miller's splitting of Stiefel manifolds. The proof uses the theory of orthogonal calculus developed by M. Weiss. The argument is inspired by an old argument of Goodwillie for a different, but closely related, general splitting result.