User's guide to equivariant methods in combinatorics. II (Q2774637)

This paper is a continuation of the author's article [Publ. Inst. Math., Nouv. Sér. 59(73), 114-130 (1996; Zbl 0946.52001)]. In both papers the author presents the methods of equivariant topology which provided necessary tools for the recent solutions of several problems in Combinatorics and Combinatorial Geometry. Namely, quite often some combinatorial problem is reduced to the non-existence of the certain equivariant mapping and so it could be treated by the methods of equivariant Topology.NEWLINENEWLINENEWLINEIn the previous paper the author introduced the complexity of a space -- an integer-valued function describing how a group acts on a space. The index function considered in this paper takes values in the ideal of the cohomology ring of the classifying space of the group acting on the space.NEWLINENEWLINENEWLINEAlso the methods of equivariant obstruction theory are considered and compared with the methods of index theory.NEWLINENEWLINENEWLINEThe author illustrates the power of these methods with several combinatorial applications including the topological Tverberg problem and the equipartition problem.NEWLINENEWLINENEWLINEThis presentation is very nice, self-contained and user-friendly and could be interesting both for experts and non-experts having in mind the applications of these ideas in the areas of their interest.