3-Sphären mit kleinen Eckenvalenzen

Ohne Zusammenfassung

---

Herrn Professor Dr. Dr.h.c.mult. Otto Haupt mit den besten Wünschen zum 100. Geburtstag gewidmet     

Ferrocene derivatives, LXXI; Stereochemistry of metallocenes, LVI Synthesis and structure of optically active ferrocenylaminoalcohols

The reaction of enantiomerically pure 1,2-(-N,N-dimethylamino)-tetramethylene ferrocene (4) with butyllithium and subsequent treatment with either benzophenone or paraformaldehyde has yielded the aminoalcohols 6–11. The absolute configurations of 4 and 6–11 were deduced from the X-ray structures of the (R,R)-tartrate of 4 (4-T) and the aminoalcohol 6. In addition the optical purity of 4 was shown to be at least 95% by transformation into the ketone 2. In solution the annelated six-membered ring in compounds 4 and 6–11 was found to adopt a preferred half-chair conformation very similar to that found in the solid state structures of 4-T and 6.     

An O(n log n) algorithm for the convex bipartite matching problem

An efficient algorithm to solve the maximum cardinality matching problem in convex bipartite graphs is presented. In the algorithm use is made of a special data structure based on a binary heap.     

Réduction des tores déployés par une extension modérément ramifiée

We study the connected component of the special fiber of the Néron model of a torus split over a tamely ramified extension. It turns out to be a product of Witt vectors of finite length, explicitly calculable. We are thus able to correct a result presented in Kunyavskii and Sansuc (C. R. Acad. Sci. Paris, Ser. I 324 (1997) 307–312). To cite this article: C. Buchheim, H. Frommer, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Cusp closing in rank one symmetric spaces

We investigate conditions under which cusps of pinched negative curvature can be closed as manifolds or orbifolds with nonpositive sectional curvature. We show that all cusps of complex hyperbolic type can be closed in this way whereas cusps of quaternionic or Cayley hyperbolic type cannot be closed. For cusps of real hyperbolic type we derive necessary and sufficient closing conditions. In this context we prove that a noncompact finite volume quotient of a rank one symmetric space can be approximated in the Gromov Hausdorff topology by closed orbifolds with nonpositive curvature if and only if it is real or complex hyperbolic. Using cusp closing methods we obtain new examples of real analytic manifolds of nonpositive sectional curvature and rank one containing flats. By the same methods we get an explicit resolution of the singularities in the Baily–Borel resp.Siu–Yau compactification of finite volume quotients of the complex hyperbolic space. Oblatum 2-IX-1994 & 7-VIII-1995