Homologie cyclique, principe de Selberg et pseudo-coefficient.
The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called commutative -group), is introduced. Commutative -groups are studied from the set-theoretical point of view and from the point of view of free groups. Commutativity of the operator which is a special kind of inverse limit and factorization, is proved. Tensor product is defined, commutativity of direct product (also a free group construction and tensor product) with the special...
A homology theory of Banach manifolds of a special form, called FSQL-manifolds, is developed, and also a homological degree of FSQL-mappings between FSQL-manifolds is introduced.
We will explain how some new algebraic solutions of the sixth Painlevé equation arise from complex reflection groups, thereby extending some results of Hitchin and Dubrovin-- Mazzocco for real reflection groups. The problem of finding explicit formulae for these solutions will be addressed elsewhere.