Suspensions of homology spheres

This article is one of three highly influential articles on the topology of manifolds written by Robert D. Edwards in the 1970's but never published. It presents the initial solutions of the fabled Double Suspension Conjecture. (The other two articles are: 'Approximating certain cell-like maps by homeomorphisms' and 'Topological regular neighborhoods') The manuscripts of these three articles have circulated privately since their creation. The organizers of the Workshops in Geometric Topology (http://www.math.oregonstate.edu/~topology/workshop.htm) with the support of the National Science Foundation have facilitated the preparation of electronic versions of these articles to make them publicly available. The second and third articles are still in preparation. The current article contains four major theorems: I. The double suspension of Mazur's homology 3-sphere is a 5-sphere, II. The double suspension of any homology n-sphere that bounds a contractible (n+1)-manifold is an (n+2)-sphere, III. The double suspension of any homology 3-sphere is the cell-like image of a 5-sphere. IV. The triple suspension of any homology 3-sphere is a 6-sphere. Edwards' proof of I. was the first evidence that the suspension process could transform a non-simply connected manifold into a sphere, thereby answering a question that had puzzled topologists since the mid-1950's if not earlier. Results II, III and IV represent significant advances toward resolving the general double suspension conjecture: the double suspension of every homology n-sphere is an (n+2)-sphere. [That conjecture was subsequently proved by J. W. Cannon (Annals of Math. 110 (1979), 83-112).]Comment: 84 pages, 27 figure

First Lattice Study of the NN-P11(1440)P_{11}(1440) Transition Form Factors

Experiments at Jefferson Laboratory, MIT-Bates, LEGS, Mainz, Bonn, GRAAL, and Spring-8 offer new opportunities to understand in detail how nucleon resonance ($N^*$) properties emerge from the nonperturbative aspects of QCD. Preliminary data from CLAS collaboration, which cover a large range of photon virtuality $Q^2$ show interesting behavior with respect to $Q^2$ dependence: in the region $Q^2 \le 1.5 {GeV}^2$, both the transverse amplitude, $A_{1/2}(Q^2)$, and the longitudinal amplitude, $S_{1/2}(Q^2)$, decrease rapidly. In this work, we attempt to use first-principles lattice QCD (for the first time) to provide a model-independent study of the Roper-nucleon transition form factor.Comment: 4 pages, 2 figures, double colum

C-kit expression in the salivary gland neoplasms adenoid cystic carcinoma, polymorphous low-grade adenocarcinoma, and monomorphic adenoma

Objective. Differentiating between adenoid cystic carcinomas (ACCs), polymorphous low-grade adenocarcinomas (PLGAs), and the monomorphic adenomas (including canalicular adenomas, trabecular adenomas, and basal cell adenomas) can present a diagnostic challenge, especially when examining tissue obtained from small incisional or fragmented biopsies. Recent studies have revealed that overexpression of the tyrosine kinase receptor protein c-kit occurs in a narrow subset of malignant neoplasms, including gastrointestinal stromal tumors, myeloid leukemias, seminomas, and ACCs. C-kit reportedly is not expressed in PLGAs. We compared the expression of the c-kit antigen in the malignant salivary gland neoplasms ACC and PLGA with its expression in salivary gland monomorphic adenoma (including canalicular adenoma and basal cell adenoma). Study design. Formalin-fixed paraffin-embedded sections of 49 salivary gland neoplasms (17 monomorphic adenomas, 17 PLGAs, and 15 ACCs) accessioned between 1989 and 2002 were retrieved from the files of the Department of Pathology, Long Island Jewish Medical Center, and were stained with an anti-c-kit polyclonal antibody. Results. C-kit reactivity was uniformly positive in the cytoplasm of luminal neoplastic cells in ACCs (15/15, 100%). Positive reactivity was also identified in the majority of PLGAs (16/17, 94%), with at least 25% of the tumor cells being positive. Similar reactivity was seen in monomorphic adenomas (16/17, 94%). Conclusions. In contrast to previous reports, we find that c-kit expression was not restricted to ACC but was expressed in all 3 tumor types evaluated (ACC, PLGA, and monomorphic adenoma). Therefore, c-kit does not appear to be a useful marker for distinguishing between either ACC and PLGA in equivocal cases, or in benign and malignant salivary gland neoplasms