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 th...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.展开更多
We confirm the Halperin-Carlsson conjecture for free Z_p-torus actions(p is a prime) on 2-dimensional finite CW-complexes and free Z_2-torus actions on closed 3-manifolds.
基金supported by National Natural Science Foundation of China(Grant No.11371188)the PAPD(Priority Academic Program Development)of Jiangsu Higher Education Institutions
文摘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.
基金supported by National Natural Science Foundation of China (Grant No. 11371188)the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘We confirm the Halperin-Carlsson conjecture for free Z_p-torus actions(p is a prime) on 2-dimensional finite CW-complexes and free Z_2-torus actions on closed 3-manifolds.