Cohomology algebra of the orbit space of some free actions on spaces of cohomology type (a, b)

Details Cohomology algebra of the orbit space of some free actions on spaces of cohomology type (a, b) Cohomology algebra of the orbit space of some free actions on spaces of cohomology type (a, b)

2008-08-11

arxiv.org/abs/0808.1319v1

Mathematics

Algebraic Topology

11 pages

Scientific paper

Let X be a finitistic space with non-trivial cohomology groups H^in(X;Z)=Z with generators v_i, where i = 0, 1, 2, 3. We say that X has cohomology type (a, b) if v_1^2 = av_2 and v_1v_2 = bv_3 . In this note, we determine the mod 2 cohomology ring of the orbit space X/G of a free action of G = Z_2 on X, where both a and b are even. In this case, we observed that there is no equivariant map S^m --> X for m > 3n, where S^m 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 = S^1 on the space X of type (0, b).

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