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Homotopy commutativity
in quasitoric manifolds
Sho Hasui, Daisuke Kishimoto, Yichen Tong and Mitsunobu Tsutaya |
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Algebraic & Geometric Topology 26 (2026) 1549–1564
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DOI: 10.2140/agt.2026.26.1549
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Abstract |
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We prove that the loop space of a quasitoric manifold is homotopy commutative if and only if the underlying polytope is a product of -simplices and the characteristic matrix is equivalent to a matrix of certain type. Quasitoric manifolds over include generalized Bott manifolds, and we also construct an infinite family of homotopy nonequivalent generalized Bott manifolds over , only half of them have homotopy commutative loop spaces. In particular, for each , there are infinitely many homotopy types of -dimensional quasitoric manifolds having homotopy (non)commutative loop spaces. |
Keywords
quasitoric manifolds, loop space, homotopy commutativity,
Whitehead products, Samelson products
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Mathematical Subject Classification
Primary: 57S12
Secondary: 55P35, 55Q15
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References |
Publication
Received: 15 August 2024
Revised: 30 March 2025
Accepted: 13 April 2025
Published: 25 April 2026
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Authors |
| Sho Hasui | |
| Department of Mathematics Osaka Metropolitan University Osaka Japan |
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| Daisuke Kishimoto | |
| Faculty of Mathematics Kyushu University Fukuoka Japan |
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| Yichen Tong | |
| Institute for Theoretical
Sciences Westlake University Hangzhou China |
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| Mitsunobu Tsutaya | |
| Faculty of Mathematics Kyushu University Fukuoka Japan |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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