Cohomology algebra of the orbit space of some free actions on spaces of cohomology type ( a , b )
نویسنده
چکیده
Let X be a finitistic space with non-trivial cohomology groups H (X;Z) ∼= Z with generators vi , where i = 0, 1, 2, 3. We say that X has cohomology type (a, b) if v 1 = 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 S → 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 on the space X of type (0, b).
منابع مشابه
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