2008/08/11 by Hemant Kumar Singh, Singh, Hemant Kumar, Tej Bahadur Singh +1
Mathematics · #57S17 (Primary) 57S25 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:57S17 #msc:57S25
paper · pdf · doi:10.48550/arxiv.0808.1319
11 pages
arxiv created 2008/08/11 · openalex publication_date 2008/08/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a finitistic space with non-trivial cohomology groups Hin(X;Z)=Z with generators vi, where i = 0, 1, 2, 3. We say that X has cohomology type (a, b) if v12 = av2 and v1v2 = bv3 . In this note, we determine the mod 2 cohomology ring of the orbit space X/G of a free action of G = Z2 on X, where both a and b are even. In this case, we observed that there is no equivariant map Sm --> X for m > 3n, where Sm has the antipodal action. Moreover, it is shown that G can not act freely on space X which is of cohomology type (a, b) where a is odd and b is even. We also obtain the mod 2 cohomology ring of the orbit space X/G of free action of G = S1 on the space X of type (0, b).