Abstract
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 (ℤ p )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.
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Jin, X., Su, Y. & Yu, L. Homology roses and the D(2)-problem. Sci. China Math. 58, 1753–1770 (2015). https://doi.org/10.1007/s11425-014-4893-0
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DOI: https://doi.org/10.1007/s11425-014-4893-0
Keywords
- homology rose
- deficiency
- group cohomology
- Carlsson conjecture
- D(2)-problem
- gap
- efficiency
- Cockcroft property