Batalin-Vilkovisky algebras and the J-homomorphism

Let X be a topological space. The homology of the iterated loop space H_∗ΩnX is an algebra over the homology of the framed n-disks operad H_∗fDn [E. Getzler, Batalin-Vilkovisky algebras and two-dimensional topological field theories, Comm. Math. Phys. 159 (2) (1994) 265-285; P. Salvatore, N. Wahl, Framed discs operads and Batalin-Vilkovisky algebras, Q. J. Math. 54 (2) (2003) 213-231]. We explicitly determine this H_∗fDn-algebra structure on H_∗(ΩnX;Q). We show that the action of H_∗(SO(n)) on the iterated loop space H_∗ΩnX is related to the J-homomorphism and that the BV-operator on H_∗(Ω²X) vanishes on spherical classes only in characteristic other than 2.     

Conformal designs based on vertex operator algebras

We introduce the notion of a conformal design based on a vertex operator algebra. This notation is a natural analog of the notion of block designs or spherical designs when the elements of the design are based on self-orthogonal binary codes or integral lattices, respectively. It is shown that the subspaces of an extremal self-dual vertex operator algebra of fixed degree form conformal 11-, 7-, or 3-designs, generalizing similar results of Assmus and Mattson and Venkov for extremal doubly-even codes and extremal even lattices. Other examples are coming from group actions on vertex operator algebras, the case studied first by Matsuo. The classification of conformal 6- and 8-designs is investigated. Again, our results are analogous to similar results for codes and lattices.     

INTERPHOTORECEPTOR RETINOID-BINDING PROTEIN AND α-TOCOPHEROL PRESERVE THE ISOMERIC AND OXIDATION STATE OF RETINOL

Retinol decomposes rapidly into a number of products, including its aldehyde form, retinal, when introduced into buffer in phospholipid vesicles or ethanol. Interphotoreceptor retinoid-binding protein at low concentrations is found to protect retinol from isomerization and oxidation. The addition of alpha-tocopherol to either liposomes or an ethanolic-buffer solution also prevents decomposition. Neither of these agents interferes with the successful regeneration of pigment with 9-cis retinal in rod outer segment preparations or the restoration of sensitivity by retinoids in isolated rod photoreceptors.