(3+1)D topological phases of matter can host a broad class non-trivial defects codimension-1, 2, and 3, which the well-known point charges flux loops are special cases. The complete algebraic structure these defines higher category, be viewed as an emergent symmetry. This plays crucial role both in classification possible fault-tolerant logical operations quantum error correcting codes. In this...

We study a family of subrings, indexed by the natural numbers, of the mod p cohomology of a finite group G. These subrings are based on a family of vn-periodic complex oriented cohomology theories and are constructed as rings of generalised characteristic classes. We identify the varieties associated to these subrings in terms of colimits over categories of elementary abelian subgroups of G, na...

In this note we compute the rational cohomology ring of Sp3(Z), or equivalently, of A3, the moduli space of principally polarized abelian 3-folds. Denote the Q-Hodge structure of dimension 1 and weight −2n by Q(n). (For those not interested in Hodge theory, just interpret this as one copy of Q.) Denote by λ the first Chern class in H(A3;Q) of the Hodge bundle detπ∗Ω 1 associated to the projecti...

In this paper we first show that many braid groups of low genus surfaces have their centers as direct factors. We then give a description of centralizers and normalizers of prime order elements in pure mapping class groups of surfaces with spherical quotients using automorphism groups of fundamental groups of the quotient surfaces. As an application, we use these to show that the p-primary part...