Related papers: Finitistic Spaces with Orbit Space a Product of Pr…

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…

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…

Let G = Z2 act on a finite CW-complex X having mod 2 cohomology isomorphic to the product of quaternionic projective space and sphere HPn x Sm, n, m > or = 1. This paper is concerned with the connected fixed point sets and the orbit spaces…

Let $X$ be a finitistic space with the mod 2 cohomology of the product space of a projective space and a 4-sphere. Assume that $X$ admits a free involution. In this paper we study the mod 2 cohomology algebra of the quotient of $X$ by the…

Let $G$ be a group acting continuously on a space $X$ and let $X/G$ be its orbit space. Determining the topological or cohomological type of the orbit space $X/G$ is a classical problem in the theory of transformation groups. In this paper,…

Let $X$ be a finitistic space having the mod 2 cohomology algebra of the product of two projective spaces. We study free involutions on $X$ and determine the possible mod 2 cohomology algebra of orbit space of any free involution, using the…

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…

In this paper, we have determined the orbit spaces of free involutions on a finitistic space having mod 2 cohomology of the product of three spheres $\mathbb{S}^n\times \mathbb{S}^m \times \mathbb{S}^l, 1 \leq n \leq m \leq l$. This paper…

Let $G=\mathbb{Z}_2$ act on a finite CW-complex $X$ having mod 2 cohomology isomorphic to the product of projective space and sphere $\mathbb{F}P^n\times \mathbb{S}^m,$ where $\mathbb{F}=\mathbb{R}$ or $\mathbb{C}.$ In this paper, we have…

Let $G = \ZZ_p$, $p$ an odd prime, act freely on a finite-dimensional CW-complex $X$ with mod $p$ cohomology isomorphic to that of a lens space $L^{2m-1} (p;q_1,...,q_m)$. In this paper, we determine the mod $p$ cohomology ring of the orbit…

Suppose that G=S^1 acts freely on a finitistic space X whose mod p cohomology ring isomorphic to that of a lens space L^{2m-1}(p;q_1,...,q_m). In this paper, we determine the mod p cohomology ring of the orbit space X/G. If the…

Let X be a 1-connected compact space such that the algebra H*(X;Z/2) is generated by one single element. We compute the cohomology of the free loop space H*(LX;Z/2) including the Steenrod algebra action. When X is a projective space CP^n,…

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…

In this paper, we investigate the existence of free involutions on some Wall manifolds and we compute the mod 2 cohomology algebra of the correspondent orbit space.

Topological free involutions on S^1xS^n are classified up to conjugation. As a byproduct we obtain a new computation of the group of concordance classes of homeomorphisms of the projective space RP^n.

Let G = Z2 act on a finitistic space X having mod 2 cohomology of the product of three spheres S^n x S^m x S^l. In this paper, we have determined the fixed point sets of involutions on X. This generalizes J. C. Su [12] results for…

Let G be a finite group acting freely on a finitistic space X having cohomology type (0, b) (for example, S^n x S^{2n} is a space of type (0, 1) and the one-point union S^n V S^{2n} V S^{3n} is a space of type (0, 0)). It is known that a…

For any space X with the homotopy type of simply-connected, finite-type CW-complex, we construct an associative cochain algebra fls(X) whose cohomology algebra is isomorphic to that of LX, the free loop space on X. For certain X, we define…

For certain manifolds with an involution the mod 2 cohomology ring of the set of fixed points is isomorphic to the cohomology ring of the manifold, up to dividing the degrees by two. Examples include complex projective spaces and…

Let $G$ be a connected Lie group of rank one. In this paper the existence of free actions of group $G$ on spheres, real projective spaces and lens spaces has been studied. Most of the results have been obtained for finitistic spaces with…