Some contractible open manifolds and coverings of manifolds in dimension three

AbstractMcMillan has shown that every irreducible, contractible, open 3-manifold is the monotone union of handlebodies (only 0- and 1-handles) and that there are uncountably many such manifolds. Work by Myers and Wright shows that no irreducible, contractible, open 3-manifold different from R3 can nontrivially cover any 3-manifold when the handlebodies all have genus one or have bounded genus. We describe a family of irreducible, contractible, open 3-manifolds that we call composite Whitehead manifolds. These manifolds have the property that when written as the monotone union of handlebodies, the handlebodies must have unbounded genus. We show that there are uncountably many composite Whitehead manifolds that nontrivially cover open 3-manifolds but do not cover a compact 3-manifold. We also show that there exist uncountably many composite Whitehead manifolds which cannot nontrivially cover any 3-manifold. It is a famous unsolved problem if any irreducible, contractible, open 3-manifold different from R3 can cover a compact 3-manifold. It is unlikely that any composite Whitehead manifold covers a compact manifold, but our techniques are not strong enough to answer this question

Dense Stellar Populations: Initial Conditions

This chapter is based on four lectures given at the Cambridge N-body school "Cambody". The material covered includes the IMF, the 6D structure of dense clusters, residual gas expulsion and the initial binary population. It is aimed at those needing to initialise stellar populations for a variety of purposes (N-body experiments, stellar population synthesis).Comment: 85 pages. To appear in The Cambridge N-body Lectures, Sverre Aarseth, Christopher Tout, Rosemary Mardling (eds), Lecture Notes in Physics Series, Springer Verla

Broad Bean Mottle Virus: Identification, Serology, Host Range, and Occurrence on Faba Bean (Vicia Faba) in West Asia and Norm Africa

One of the faba bean viruses found in West Asia and North Africa was identified as broad bean mottle virus (BBMV) by host reactions, particle morphology and size, serology, and granular, often vesiculated cytoplasmic inclusions. Detailed research on four isolates, one each from Morocco, Tunisia, Sudan and Syria, provided new information on the virus. The isolates, though indistinguishable in ELISA or gel-diffusion tests, differed slightly in host range and symptoms. Twenty-one species (12 legumes and 9 non-legumes) out of 27 tested were systemically infected, and 14 of these by all four isolates. Infection in several species was symptomless, but major legumes such as chickpea, lentil and especially pea, suffered severely from infection. All 23 genotypes of faba bean, 2 of chickpea, 4 of lentil, 11 out of 21 of Phaseolus bean, and 16 out of 17 of pea were systemically sensitive to the virus. Twelve plant species were found to be new potential hosts and cucumber a new local-lesion test plant of the virus. BBMV particles occurred in faba bean plants in very high concentrations and seed transmission in this species (1.37%) was confirmed. An isolate from Syria was purified and two antisera were produced, one of which was used in ELISA to detect BBMV in faba bean field samples. Two hundred and three out of the 789 samples with symptoms suggestive of virus infection collected in 1985, 1986 and 1987, were found infected with BBMV: 4 out of 70 (4/70) tested samples from Egypt, 0/44 from Lebanon, 1/15 from Morocco, 46/254 from Sudan, 72/269 from Syria and 80/137 from Tunisia. This is the first report on its occurrence in Egypt, Syria and Tunisia. The virus is a potential threat to crop improvement in the region