Higher Smooth Surgery Structure Sets of Complex Projective Spaces, Part I

Abstract

This is the first of the two articles where we determine the higher smooth surgery structure sets of complex projective spaces (up to some extension problems) and the forgetful map to their topological versions in low dimensions. In this part, we concentrate on the free subgroup, where we obtain information in all dimensions. In the second part, we study the torsion.

30 pages, submitted to Archivum Mathematicum