Nami Arabyarmohammadi: Computing Stable Cohomotopy Groups of Stunted Projective Spaces

Abstract.

Since infinite real projective space RP∞ is a classifying space of Z2, the homotopy classes of maps X → RP∞ corresponds bijectively to isomorphism classes of line bundles on X. This makes RP∞ worth studying. We will thus partially compute the stable cohomotopy groups of this space and related stunted projective spaces. First we exhibit a nontrivial isomorphism of Ext groups, obtained by studying the cohomology of RP∞ and stunted projective spaces as modules over the Steenrod algebra. This implies that the E2 page of two Adams spectral sequences agree in an appropriate range: the one for computing the stable homotopy groups of spheres and the one for computing the stable cohomotopy of infinite stunted projective spaces, allowing us to compare the two, from which our main results will follow