On the genus of free loop fibrations over -spaces.
Let M be a closed, connected, orientable 3-manifold. Denote by n(S1 x S2) the connected sum of n copies of S1 x S2. We prove that if the homological category of M is three then for some n ≥ 1, H*(M) is isomorphic (as a ring) to H*(n(S1 x S2)).
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 paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.