Total synthesis of (-)-microcarpalide, a novel microfilament disrupting metabolite

The stereoselective total synthesis of (-)-microcarpalide, a recently discovered 10-membered lactone of fungal origin displaying a remarkable disrupting action on actin microfilaments, was accomplished by using ring-closing metathesis (RCM) as the key step for the formation of the medium-sized ring. The diene ester required for the macrocyclization reaction was assembled via DCC-mediated esterification of two suitable partners, each bearing a terminal alkene group. The alcohol fragment was synthesized from n-bromohexane through a seven-step sequence entailing two consecutive stereoselective homologations of chiral boronic esters as strategic transformations for the sequential insertion of the two stereocentres with the final S absolute configuration, using (+)-pinanediol as the chiral director; final elaboration to the desired C(11) framework envisaged treatment with an allyl Grignard reagent and oxidative cleavage of the boronic scaffold. In contrast, the acidic fragment was prepared in ten steps from d-tartaric acid, whose C(4) backbone was elongated to the required C(7) skeleton by means of two distinct Swern-Wittig oxidation-homologation sequences.     

A mild synthesis of vinyl halides and gem-dihalides using triphenyl phosphite-halogen-based reagents

A new application of (PhO)3P-halogen-based reagents to the synthesis of vinyl halides and gem-dihalides is described. Vinyl halides were prepared in good to excellent yields from enolizable ketones, whereas aldehydes afforded the corresponding gem-dihalides. The halogenation proceeded smoothly under mild conditions.     

Remarks on a Paper of M. Ochiai

This note is related to a nice short paper of M. Ochiai. We prove in a very fast way that the two-parameter family of Heegaard diagrams, constructed by Ochiai, encodes the genuine three-sphere. The result is obtained, up to isotopy, by using a sequence of only three moves in this order: a Whitehead–Zieschang reduction, a band sum and a cancellation of a handle.     

On iterated Browder-Livesay invariants

Mathematical Notes - The Browder-Livesay invariants provide obstructions to the realization of elements of Wall groups by normal maps of closed manifolds. A generalization of the iterated...     

On the pontryagin-steenrod-wu theorem

We present a short and direct proof (based on the Pontryagin-Thom construction) of the following Pontryagin-Steenrod-Wu theorem: (a) LetM be a connected orientable closed smooth (n + 1)-manifold,n≥3. Define the degree map deg: π ⁿ (M) →H ⁿ (M; ℤ) by the formula degf =f*[S ⁿ ], where [S ⁿ ] εH ⁿ (M; ℤ) is the fundamental class. The degree map is bijective, if there existsβ εH ₂(M, ℤ/2ℤ) such thatβ ·w ₂(M) ε 0. If suchβ does not exist, then deg is a 2-1 map; and (b) LetM be an orientable closed smooth (n+2)-manifold,n≥3. An elementα lies in the image of the degree map if and only ifρ ₂ α ·w ₂(M)=0, whereρ ₂: ℤ → ℤ/2ℤ is reduction modulo 2.     

Extension of Multiply Transitive Permutation Sets

Let G be a k-transitive permutation set on E and let E* = E∪{∞},∞ ? E; if G* is a (k: + 1)-transitive permutation set on E*, G* is said to be an extension of G whenever G _∝ ^* =G. In this work we deal with the problem of extending (sharply) k- transitive permutation sets into (sharply) (k + 1)-transitive permutation sets. In particular we give sufficient conditions for the extension of such sets; these conditions can be reduced to a unique one (which is a necessary condition too) whenever the considered set is a group. Furthermore we establish necessary and sufficient conditions for a sharply k- transitive permutation set (k ≥ 3) to be a group. Math. Subj. Class.: 20B20 Multiply finite transitive permutation groups 20B22 Multiply infinite transitive permutation groups     

Manifolds with Poly-Surface Fundamental Groups

We study closed topological 2n-dimensional manifolds M with poly-surface fundamental groups. We prove that if M is simple homotopy equivalent to the total space E of a Y-bundle over a closed aspherical surface, where Y is a closed aspherical n-manifold, then M is s-cobordant to E. This extends a well-known 4-dimensional result of Hillman in [14] to higher dimensions. Our proof is different from that of the quoted paper: we use Mayer-Vietoris techniques and the properties of the -theory assembly maps for such bundles.