$L$-theory and dihedral homology.

Harrison Homology, Hochschild Homology and Triples*l

We consider the following situation: a field k, a commutative k-algebra R and a left R-module M. Since R is commutative, M may also be considered as an R-R bimodule with the same operation on each side (such modules are often termed symmetric). With these assumptions we have the Harrison (co-) homology groups Harr,(R, M) (Harr*(R, M)), the Hochschild (co-) homology groups Hoch, (R, M) (Hoch*(R,...

Homology and Homotopy Theory Homotopy and Homology

1. TJ'he first step toward connecting these two basic concepts of topology was taken by L. E. J. Brouwer in 1912 by demonstrating that two continuous mappings of a two-dimensional sphere into itself can be continuously deformed into each other if and only if they have the same degree (that is, if they are equivalent from the point of view of homology theory). After having generalized Brouwer's ...

Low-lying Zeros of Dihedral L-functions

Assuming the grand Riemann hypothesis, we investigate the distribution of the lowlying zeros of the L-functions L(s, ψ), where ψ is a character of the ideal class group of the imaginary quadratic field Q( √ −D) (D squarefree, D > 3, D ≡ 3 (mod 4)). We prove that, in the vicinity of the central point s = 1/2, the average distribution of these zeros (for D −→ ∞) is governed by the symplectic dist...

PHI-DAC: protein homology database through dihedral angle conservation

UNLABELLED Finding related conformations in the Protein Data Bank is essential in many areas of bioscience. To assist this task, we designed a dihedral angle database for searching protein segment homologs. The search engine relies on encoding of the protein coordinates into text characters representing amino acid sequence, φ and ψ dihedral angles. The search engine is advantageous owing to its...

Gratings and Homology Theory