1. Homotopy commutativity in quasitoric manifolds
- Author
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Hasui, Sho, Kishimoto, Daisuke, Tong, Yichen, and Tsutaya, Mitsunobu
- Subjects
Mathematics - Algebraic Topology ,Mathematics - Geometric Topology ,57S12, 55P35, 55Q15 - Abstract
We prove that the loop space of a quasitoric manifold is homotopy commutative if and only if the underlying polytope is $(\Delta^3)^n$ and the characteristic matrix is equivalent to a matrix of certain type. We also construct for each $n\ge 2$ and a positive integer $k$, a quasitoric manifold $M(k,n)$ over $(\Delta^3)^n$ such that its loop space is homotopy commutative if and only if $k$ is even, where every quasitoric manifold over $\Delta^3$ is equivalent to $\mathbb{C} P^3$ whose loop space is homotopy commutative., Comment: 14 pages
- Published
- 2024