On the maps of one fibre space into another
We present J. Jezierski's approach to the Nielsen fixed point theory for a broad class of multivalued mappings [Je1]. We also describe some generalizations and different techniques existing in the literature.
We give a bound for the number of coincidence of two morphisms between given compact Riemann surfaces (complete complex algebraic curves). Our results generalize well known facts about the number of fixed points of an automorphism.
The problem of the characterization of graded Lie algebras which admit a realization as the homotopy Lie algebra of a space of type is discussed. The central results are formulated in terms of varieties of structure constants, several criterions for concrete algebras are also deduced.
Let LX be the space of free loops on a simply connected manifold X. When the real cohomology of X is a tensor product of algebras generated by a single element, we determine the algebra structure of the real cohomology of LX by using the cyclic bar complex of the de Rham complex Ω(X) of X. In consequence, the algebra generators of the real cohomology of LX can be represented by differential forms on LX through Chen’s iterated integral map. Let be the circle group. The -equivariant cohomology...