Homotopy groups of polyhedral products
组织者
演讲者
Lewis Stanton
时间
2026年04月30日 15:00 至 16:00
地点
A3-4-301
线上
Zoom 518 868 7656
(BIMSA)
摘要
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.