Transfer systems and weak factorization systems

Abstract: $N_\infty$ operads over a group G encode homotopy commutative operations together with a class of equivariant transfer (or norm) maps. Their homotopy theory is given by transfer systems, which are certain discrete objects that have a rich combinatorial structure defined in terms of the subgroup lattice of G. In this talk, we will show that when G is finite Abelian, transfer systems are in bijection with weak factorization systems on the poset category of subgroups of G. This leads to an involution on the lattice of transfer systems, generalizing the work of Balchin–Bearup–Pech–Roitzheim for cyclic groups of squarefree order. We will conclude with an enumeration of saturated transfer systems and comments on the Rubin and Blumberg–Hill saturation conjecture.

This is joint work with Evan Franchere, Usman Hafeez, Peter Marcus, Kyle Ormsby, Weihang Qin, and Riley Waugh.

algebraic topology

Audience: researchers in the topic

Online algebraic topology seminar

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