Abstract This paper deals with certain results on the number of smooth structures quaternionic projective spaces, obtained through computation inertia groups and their analogues, which in turn are computed using techniques from stable homotopy theory. We show that concordance group is trivial dimension 20, but there many examples high dimensions where non-trivial. extend these to computations c...

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0. The homotopy groups of CW complexes are, in general, much more mysterious than the stable homotopy groups. A notable exception is the case of spheres or cases when the unstable Adams spectral sequence can be utilized. The problem is clearest in the case of a 2-cell complex S ∪ e. Very little knowledge of such spaces was known before the work of Cohen, Moore, and Neisendorfer who analyzed the...

A description of homotopy groups of the 2-dimensional sphere in terms of combinatorial group theory was discovered by the second author in 1994 and given in his thesis [25], with a published version in [27]. In this article we give a combinatorial description of the homotopy groups of k-dimensional spheres with k ≥ 3. The description is given by identifying the homotopy groups as the center of ...