Stiefel-Whitney classes and toral actions

Certain Stiefel-Whitney classes of manifolds with smooth, effective toral actions are shown to be computable in terms of Poincare duals of fixed point sets of isotropy subgroups. As an application the toral degrees of symmetry of certain Dold manifolds are determined.     

Raney-Co mediated reductive cyclization of an alpha,beta-unsaturated nitrile

An expedient, five step synthesis of caprolactam 1 is reported starting from natural L-homoserine. The key step is a chemoselective reductive cyclization of alpha,beta-unsaturated nitrile 10 mediated by Raney-Co type metals. This hydrogenation is extensively investigated in order to account for the observed product distribution and yields.     

Chiral C2-Symmetric CuII Complexes as Catalysts for Enantioselective Hetero-Diels–Alder Reactions

Air-stable and recyclable , the Cu^II–(bis)oxazoline complex 1 efficiently catalyzes diastereo- and enantioselective hetero-Diels–Alder reactions between β,γ-unsaturated α-keto acid derivatives 2 and vinyl ethers for the synthesis of substituted dihydropyrans 3 [Eq. (1)]. Results of the crystal structure analysis of 1 in combination with calculations on model compounds indicate the formation of a reactive intermediate through replacement of the two H₂O ligands with a chelating substrate. X=OEt, N(OMe)Me; R=alkyl, aryl, alkoxy, thiobenzyl.     

Synthesis of the HCV protease inhibitor Vaniprevir (MK-7009) using ring-closing metathesis strategy

A highly efficient synthesis of Vaniprevir (MK-7009) has been accomplished in nine linear steps and 55% overall yield. The key features of this synthesis include a cost-effective synthesis of the isoindoline subunit and efficient construction of the 20-membered macrocyclic core of Vaniprevir (MK-7009) utilizing ring-closing metathesis technology. A high-performing ring-closing metathesis protocol has been achieved by simultaneous slow addition of the ruthenium catalyst (0.2 mol %) and the diene substrate at a concentration of 0.13 M.     

A primary obstruction to topological embeddings¶and its applications

For a proper continuous map f:M→N between topological manifolds M and N with m≡ dimM < dimN≡m+k, a primary obstruction to topological embeddings θ(f) ∈H ^c _{m − k} (M; Z ₂) has been defined and studied by the authors in {9, 8, 2, 3], where H ^c _* denotes the singular homology with closed support. In this paper, we study the obstruction from the viewpoint of differential topology and give various applications. We first give some characterizations of embeddings among generic differentiable maps, which are refinements of the results in [9, 10]. Then we give a result concerning the number of connected components of the complement of the image of a codimension-1 continuous map with a normal crossing point, which generalizes the results in [6, 4, 5, 9]. Finally we give a simple proof of a theorem of Li and Peterson [20] about immersions of m-manifolds into (2m-1)-manifolds. Received: 3 December 1999 / Revised version: 10 October 2000     

A biocatalytic/reductive etherification approach to substituted piperidinyl ethers

A synthetically useful protocol has been developed for the preparation of highly functionalized piperidinyl ethers. Biocatalytic reduction of cyclhexanones 7, 10, and 14 allows for the preparation of both cis- and trans diastereomers with an extremely high degree of stereochemical control. Reductive etherification of the corresponding trimethylsilylethers with 1-(benzyloxycarbonyl)-4-piperidinone 17 in the presence of triethylsilane and catalytic TMSO-Tf provides the desired piperidinyl ethers in good to excellent yields. Finally hygrogenolysis of the nitrogen protecting group leads to piperidinyl ethers in near quantitative yields. Application of the methodology to a range of piperidinyl ethers, including the core scaffolds of diphenylpyraline and ebastine, is also described.