Homotopy groups of polyhedral products
Organizers
Speaker
Lewis Stanton
Time
Thursday, April 30, 2026 3:00 PM - 4:00 PM
Venue
A3-4-301
Online
Zoom 518 868 7656
(BIMSA)
Abstract
A conjecture of Moore asserts a deep connection between the torsion and torsion-free parts of the homotopy groups of any simply connected finite CW complex. This is closely related to a conjecture of Anick, which asserts a connection between the homotopy groups of such spaces and the homotopy groups of spheres.
Much work has been done recently to verify these conjectures in the context of polyhedral products. These are natural subspaces of Cartesian products of spaces indexed by a simplicial complex, and they unify constructions across mathematics.
In this talk, I will summarise the work of Hao, Sun, and Theriault which verified Moore's conjecture for an important class of polyhedral products. I will then discuss work of various authors on Anick's conjecture, culminating in joint work with Vylegzhanin which verifies the conjecture for most polyhedral products.
Much work has been done recently to verify these conjectures in the context of polyhedral products. These are natural subspaces of Cartesian products of spaces indexed by a simplicial complex, and they unify constructions across mathematics.
In this talk, I will summarise the work of Hao, Sun, and Theriault which verified Moore's conjecture for an important class of polyhedral products. I will then discuss work of various authors on Anick's conjecture, culminating in joint work with Vylegzhanin which verifies the conjecture for most polyhedral products.