arXiv subjects

Anju Kumari

Publications and source records attributed to Anju Kumari.

4 recordsLinked to original sources

arXiv2024

Finitistic Spaces with Orbit Space a Product of Projective Spaces

Let G = Z2 act freely on a nitistic space X. If the mod 2 cohomology of X is isomorphic to the real projective space RP^{2n+1} (resp. complex projective space CP^{2n+1}) then the mod 2 cohomology of orbit spaces of these free actions are RP1 x CPn (resp. RP2 x HPn) [7]. In this paper, we have discussed converse of these results. We have showed that if the mod 2 cohomology of the orbit space X/G is RP1 x CPn (resp. RP2 x HPn) then the mod 2 cohomology of X is RP^{2n+1} or S1 x CPn (resp. CP^{2n+1} or S2 x HPn). A partial converse of free involutions on the product of projective spaces RPn x RP2m+1 (resp. CPn x CP2m+1) are also discussed.

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arXiv2023

Finitistic Spaces with the Orbit Space FP^n x S^m

Let G = S^d, d = 0, 1 or 3, act freely on a finitistic connected space X. This paper gives the cohomology classification of X if a mod 2 or rational cohomology of the orbit space X/G is isomorphic to the product of a projective space and sphere FP^n x S^m, where F = R, C or H, respectively. For a free involution on X, a lower bound of covering dimension of the coincidence set of a continuous map f: X -> R^k is also determined.

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arXiv2021

Fixed point Free Actions of Spheres and Equivariant maps

This paper generalizes the concept of index and co-index and some related results for free actions of G = S0 on a paracompact Hausdorff space which were introduced by Conner and Floyd. We define the index and co-index of a finitistic free G-space X, where G = Sd , d = 1 or 3 and prove that the index of X is not more than the mod 2 cohomology index of X. We observe that the index and co-index of a (2n + 1)-sphere (resp. (4n+3)-sphere) for the action of componentwise multiplication of G = S1 (resp. S3) is n. We also determine the orbit spaces of free actions of G = S3 on a finitistic space X with the mod 2 cohomology and the rational cohomology product of spheres. The orbit spaces of circle actions on the mod 2 cohomology X is also discussed. Using these calculation, we obtain an upper bound of the index of X and the Borsuk-Ulam type results.

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arXiv2021

Cohomology Classification of Spaces with Free S3 Actions

This paper gives the cohomology classification of finitistic spaces X equipped with free actions of the group G = S3 and the orbit space X/G is the integral or mod 2 cohomology quaternion projective space HPn. We have proved that X is the integral or mod 2 cohomology (4n+3)-sphere or the product of 3-sphere and quaternion projective space HPn. Similar results for G = S1 actions are also discussed.

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