The Goodwillie tower for S^1 and Kuhn's theorem

We analyze the homological behavior of the attaching maps in the 2-local Goodwillie tower of the identity evaluated at S^1. We show that they exhibit the same homological behavior as the James-Hopf maps used by N. Kuhn to prove the 2-primary Whitehead conjecture. We use this to prove a calculus form of the Whitehead conjecture: the Whitehead sequence is a contracting homotopy for the Goodwillie tower of S^1 at the prime 2.Comment: v2: 23 pages, clarified exposition in many parts, to appear in AG

Some root invariants at the prime 2

The first part of this paper consists of lecture notes which summarize the machinery of filtered root invariants. A conceptual notion of "homotopy Greek letter element" is also introduced, and evidence is presented that it may be related to the root invariant. In the second part we compute some low dimensional root invariants of v_1-periodic elements at the prime 2.Comment: This is the version published by Geometry & Topology Monographs on 29 January 200

Asbestos Trust Transparency

Originally and for many years, the primary defendants in asbestos cases were companies that mined asbestos or manufactured amphibole-containing thermal insulation. Hundreds of thousands of claims were filed against the major asbestos producers, such as Johns-Manville Corp., Owens Corning Corp., and W.R. Grace & Co. By the late 1990s, asbestos litigation had reached such proportions that the U.S. Supreme Court noted the “elephantine mass” of cases and referred to the litigation as a “crisis.” Mass filings pressured “most of the lead defendants and scores of other companies” into bankruptcy, including virtually all manufacturers of asbestos-containing thermal insulation. Following a 2000–2002 wave of bankruptcies among asbestos manufacturers, plaintiffs’ lawyers began “a search for new recruits to fill the gap in the ranks of defendants.” Many of today’s asbestos defendants are formerly peripheral or new defendants associated with chrysotile-containing products “such as gaskets, pumps, automotive friction products, and residential construction products.” One plaintiffs’ attorney described the asbestos litigation as an “endless search for a solvent bystander.” This Article argues for legislation, such as that enacted in many states, that requires asbestos plaintiffs to pursue quick compensation from the trusts and allows trust-related exposures and compensation to be properly accounted for in asbestos-related personal injury cases. States with substantial asbestos litigation, such as California, Illinois, New York, and Missouri, need the legislation the most

Isogenies of elliptic curves and the Morava stabilizer group

Let MS_2 be the p-primary second Morava stabilizer group, C a supersingular elliptic curve over \br{FF}_p, O the ring of endomorphisms of C, and \ell a topological generator of Z_p^x (respectively Z_2^x/{+-1} if p = 2). We show that for p > 2 the group \Gamma \subseteq O[1/\ell]^x of quasi-endomorphisms of degree a power of \ell is dense in MS_2. For p = 2, we show that \Gamma is dense in an index 2 subgroup of MS_2.Comment: 16 pages, to appear in J. Pure Appl. Al