Homotopy commutativity in quasitoric manifolds
Abstract
We prove that the loop space of a quasitoric manifold is homotopy commutative if and only if the underlying polytope is a product of $3$-simplices $(Δ^3)^n$ and the characteristic matrix is equivalent to a matrix of certain type. Quasitoric manifolds over $(Δ^3)^n$ include generalized Bott manifolds, and we also construct an infinite family of homotopy nonequivalent generalized Bott manifolds over $(Δ^3)^n$, only half of them have homotopy commutative loop spaces. In particular, for each $n\ge 2$, there are infinitely many homotopy types in $6n$-dimensional quasitoric manifolds having homotopy (non)commutative loop spaces.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Advanced Topics in Algebra
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Publisher
- Mathematical Sciences Publishers
- Volume
- 26
- Issue
- 4
- Pages
- 1549–1564
- Publication date
- 25 April 2026
- Language
- EN