Loop homology of bi-secondary structures

Free loop space and homology

The aim of this paper is to explain the relationship between the (co)homology of the free loop space and the Hochschild homology of its singular cochain algebra. We introduce all the relevant technical tools, namely simplicial and cyclic objects, and we provide the various steps of the proofs, which are scattered around in the literature. This paper can be seen as a companion to the paper “Cycl...

0 the Homology of Iterated Loop Spaces

Bi–Hamiltonian Structures and Solitons

Methods in Riemann–Finsler geometry are applied to investigate bi–Hamiltonian structures and related mKdV hierarchies of soliton equations derived geometrically from regular Lagrangians and flows of non–stretching curves in tangent bundles. The total space geometry and nonholonomic flows of curves are defined by Lagrangian semisprays inducing canonical nonlinear connections (N–connections), Sas...

Secondary structures of DNA.

In view of the differences of the X-ray diffraction patterns for DNA fibers at 66 and 92 per cent relative humidities, it is proposed that the secondary structure of DNA consists of two partially intercalated double helices at 92 per cent. Possible biological implications are discussed.

Loop Algebras and Bi-integrable Couplings∗

A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations. The variational identities under non-degenerate, symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings. A special case of the s...