Mathematics

Projective spaces are among the most important geometric objects in mathematics. An example is n-dimensional real projective space, obtained from the n-sphere by identifying antipodal points.

We will investigate how the essential geometric cells of various dimensions in a projective space are glued to one another, as detected by cohomology operations that reflect specific geometric attachments.

We find a minimal set of generators and relations modulo two for the cells and attachments, that is, a minimal presentation for the cohomology of a real projective space as a module over the Steenrod algebra of cohomology operations.

The talk will be readily accessible to anyone with an undergraduate mathematics background.