Homology, Homotopy and Applications

Volume 22 (2020)

Number 2

Constructions of self-maps of $\operatorname{SU}(4)$ via Postnikov towers

Pages: 387 – 399

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n2.a23

Authors

Jim Fowler (Department of Mathematics Ohio State University Columbus, Oh., U.S.A.)

Chris Kennedy (Department of Mathematics Ohio State University Columbus, Oh., U.S.A.)

Abstract

Cohomology operations restrict the degree of a self-map of $\operatorname{SU}(4)$ to be either odd or a multiple of $8$; we find self-maps realizing these possible degrees. The notion of the degree of a self-map can be refined to a notion of multidegree which records the effect of the self-map on each of the generators of $H^{\star} (\operatorname{SU}(4))$. We find restrictions on the possible multidegrees of self-maps of $\operatorname{SU}(4)$ and, via Postnikov towers, build self-maps stage-by-stage realizing the possible multidegrees.

Keywords

mapping degree sets, Postnikov towers

2010 Mathematics Subject Classification

55M25, 57N65, 57T10

Received 15 August 2019

Accepted 12 December 2019

Published 20 May 2020