摘要
For a commutative ring R with a unit, an R-homology rose is a topological space whose homology groups with R-coefficients agree with those of a bouquet of circles. In this paper, we study some special properties of the fundamental groups of R-homology roses and their covering spaces, from which we obtain some results supporting the Carlsson conjecture on free(Zp)ractions. In addition, we discuss how to search candidates of the counterexamples of Wall's D(2)-problem among R-homology roses and R-acyclic spaces and propose some candidates.
For a commutative ring R with a unit, an R-homology rose is a topological space whose homology groups with R-coefficients agree with those of a bouquet of circles. In this paper, we study some special properties of the fundamental groups of R-homology roses and their covering spaces, from which we obtain some results supporting the Carlsson conjecture on free （Zp）r actions. In addition, we discuss how to search candidates of the counterexamples of Wall＇s D（2）-problem among R-homology roses and R-acyclic spaces and propose some candidates.
基金
supported by National Natural Science Foundation of China(Grant No.11371188)
the PAPD(Priority Academic Program Development)of Jiangsu Higher Education Institutions
