Embeddings from the point of view of immersion theory: Part II

Let M and N be smooth manifolds. For an open V of M let emb(V,N) be the space of embeddings from V to N. By results of Goodwillie and Goodwillie-Klein, the cofunctor V |--> emb(V,N) is analytic if dim(N)-dim(M) > 2. We deduce that its Taylor series converges to it. For details about the Taylor series, see Part I.Comment: 16 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper4.abs.htm

Calculus of functors and model categories

The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure. In this paper we construct various localizations of the projective model structure and also give a variant for functors from simplicial sets to spectra. We apply these model categories in the study of calculus of functors, namely for a classification of polynomial and homogeneous functors. In the $n$-homogeneous model structure, the $n$-th derivative is a Quillen functor to the category of spectra with $\Sigma_n$-action. After taking into account only finitary functors -- which may be done in two different ways -- the above Quillen map becomes a Quillen equivalence. This improves the classification of finitary homogeneous functors by T. G. Goodwillie.Comment: 22 pages. Exposition is substantially improved. Few minor mistakes are correcte

The Shakers in Eighteenth-Century Newspapers, Part Three: “Calvin” versus “A Lover of Truth,” Abusing Caleb Rathbun, the Death of Joseph Meacham and the Tale of His Sister

Accounts of the Shakers in eighteenth-century American newspapers help to shed light on the murky early history of the sect in the United States. They range from openly hostile to mildly sympathetic, and often provide details about the Shakers and Shaker life that are not found in the sect’s relatively meager eighteenth-century manuscript record. This article, the third and final in a series, will examine newspaper items relevant to the Shakers in the extraordinarily busy news years of 1796 and 1797

Light and Dark Sides of Spiritualism: The Eddy Brothers and the Shakers

In his 1899 work Manifestation of Spiritualism Among the Shakers Elder Henry Blinn reflected on the marvelous events that dominated life in Shaker communities from 1837 into the 1850s. Looking back on these events fifty years later Blinn realized that what the Shakers experienced was but a precursor to the popular movement called Spiritualism that swept America and Europe in the second half of the nineteenth century. In fact, the experience of the Shakers as progenitors of, and then participants in, the Spiritualist movement, is far more complex than Blinn’s retrospective stated. This article will examine one dimension of that experience—the interaction of individual Shakers with the notorious Vermont mediums, the Eddy Brothers. This interesting episode in Shaker history involved both Blinn and Evans, as well as many other Shakers. The Shakers relationship with the Eddys provides substantial evidence of their attitude toward the Spiritualist movement as it evolved beyond the realm of the Shaker communities

A Postscript to Writings of Shaker Apostates and Anti-Shakers, 1782-1850: New Light on Benjamin West, William Scales, Benjamin Green, and Zebulon Huntington

The collection, annotation, and editorial writing associated with the set of apostate and anti-Shaker writings I published in 2013 consumed much of my free time for two years prior. Months of intensive research yielded quite a bit of new information about many heretofore obscure ex- or anti-Shakers, but I knew as I concluded my work that much was left to be found. This brief piece will share some of what has since come to light about Benjamin West, William Scales, and Benjamin Green (whose texts were in the collection), as well as the discovery of a previously unknown Shaker apostate work by Zebulon Huntington

Calculus III: Taylor Series

We study functors from spaces to spaces or spectra that preserve weak homotopy equivalences. For each such functor we construct a universal n-excisive approximation, which may be thought of as its n-excisive part. Homogeneous functors, meaning n-excisive functors with trivial (n-1)-excisive part, can be classified: they correspond to symmetric functors of n variables that are reduced and 1-excisive in each variable. We discuss some important examples, including the identity functor and Waldhausen's algebraic K-theory.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper19.abs.htm