2013/11/27 by Xifeng Jin, XiFeng Jin, Yang Su +1
Computer Science · Mathematics · #Commutative property #Conjecture #Counterexample #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Singular homology #Topological and Geometric Data Analysis #math.AT #math.GT #msc:57M07 #msc:57M10 #msc:57M20 #msc:57Q12
paper · pdf · doi:10.1007/s11425-014-4893-0
published as Science China Mathematics 58 (2015), no. 8, 1753-1770 · 26 pages, no figure; some new results are added to the previous version
arxiv created 2013/11/27 · openalex publication_date 2014/10/24 · arxiv updated 2016/03/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 cirlces. In this paper, we study some special properties of covering spaces and fundamental groups of R-homology roses, from which we obtain some result supporting the Carlsson conjecture on free (Zp)r actions. In addition, for a group G and a field F, we define an integer called the F-gap of G, which is an obstruction for G to be realized as the fundamental group of a 2-dimensional F-homology rose. Furthermore, we discuss how to search candidates of the counterexamples of Wall's D(2)-problem among F-homology roses and F-acyclic spaces.