The Character Map in Equivariant Twistorial Cohomotopy (2011.06533v2)

Abstract: The fundamental notion of non-abelian generalized cohomology gained recognition in algebraic topology as the non-abelian Poincar\'e-dual to "factorization homology", and in theoretical physics as providing flux-quantization for non-linear Gauss laws. However, already the archetypical example -- unstable Cohomotopy, first studied almost a century ago by Pontrjagin -- may remain underappreciated as a cohomology theory. In illustration and amplification of its cohomological nature, we construct the non-abelian generalization of the Chern character map on $\mathbb{Z}_2$-equivariantized 7-Cohomotopy -- in fact on its "twistorial" version classified by complex projective 3-space -- essentially by computing its equivariant Sullivan model, and we highlight some interesting integral cohomology classes which are extracted this way. We end with an outlook on the application of this result to the rigorous deduction of anyonic quantum states on M5-branes wrapped over Seifert 3-orbifolds.