Let S 0 (p) denote the sphere spectrum localized at an odd prime p. Then we have the first beta element β 1 ∈ π 2p 2 −2p−2 (S 0 (p)), whose cofiber we denote by W. We also consider a generalized Smith-Toda spectrum V r characterized by BP * (V r) = BP * /(p, v r 1). In this note, we show that an element of π * (V r ∧ W) gives rise to a beta element of… (More)
The Ravenel spectra T (m) for non-negative integers m interpolate between the sphere spectrum and the Brown-Peterson spectrum. Let L 2 denote the Bousfield-Ravenel localization functor with respect to v −1 2 BP. In this paper, we determine the homotopy groups π * (L 2 T (m) : Z/2) = [M 2 , L 2 T (m)] * for m > 1, where M 2 denotes the modulo two Moore… (More)
On the homotopy groups of E(n)–local spectra with unusual invariant ideals HIROFUMI NAKAI KATSUMI SHIMOMURA Let E(n) and T(m) for nonnegative integers n and m denote the Johnson–Wilson and the Ravenel spectra, respectively. Given a spectrum whose E(n) * –homology is E(n) * (T(m))/(v 1 ,. .. , v n−1), then each homotopy group of it estimates the order of… (More)
In , Miller, Ravenel and Wilson defined generalized beta elements in the E 2-term of the Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres, and in , Oka showed that the beta elements of the form β tp 2 /r for positive integers t and r survives to the stable homotopy groups at a prime p > 3, when r ≤ 2p − 2 and r ≤ 2p… (More)
Anomalies of the appendix are extremely rare, and a horseshoe appendix is even rarer. A literature search has revealed only five reported cases. In this report, we present a case of a horseshoe appendix.A 78-year-old man was referred for further examination following a positive fecal occult blood test. A mass in his ascending colon was detected on… (More)
Pyogenic liver abscess (PLA) complicated by inferior vena caval (IVC) thrombosis is rare but life-threatening. We experienced a case of PLA complicated by an IVC thrombus close to the right atrium after pancreatoduodenectomy. A 75-year-old man had undergone pancreatoduodenectomy with modified-Child reconstruction for pancreatic cancer 3 years prior, and no… (More)
In , Bousfield studied a lattice (Bousfield lattice) on the stable homotopy category of spectra, and in , Hovey and Palmieri made the retract conjecture on the lattice. In this paper we generalize the Bousfield lattice and the retract conjecture to the ones on a monoid. We also determine the structure of typical examples of them, which satisfy the… (More)
We deduce the essential elements α 1 β p−2 1 γt for t > p with t ̸ = 0, 1 modulo (p) of the homotopy groups of spheres from result of C-N. Lee, which states that α 1 β p−2 1 γt is essential for t < p.
Let p be a prime number greater than three. In the p-component of stable homotopy groups of spheres, Oka constructed a beta family from a v 2-periodic map on a four cell complex. In this paper, we construct another beta family in the groups at a prime p greater than five from a v 2-periodic map on a eight cell complex.
Let L 2 denote the stable homotopy category of v −1 2 BP-local spectra at the prime three. In , it is shown that the Picard group of L 2 consisting of isomorphic classes of invertible spectra is isomorphic to either the direct sum of Z and Z/3 or the direct sum of Z and two copies of Z/3. In this paper, we conclude the Picard group is isomorphic to the… (More)