arXiv Open Access 2025

Anick's conjecture for polyhedral products

Lewis Stanton Fedor Vylegzhanin

Lihat Sumber

Abstrak

We develop a method for studying the pointed loop space of general polyhedral products, showing that many properties are determined by the moment-angle complex. To apply the method, we show that localised away from a finite set of primes, the loop space of a moment-angle complex is homotopy equivalent to a product of loops on spheres. As a consequence, we give p-local loop space decompositions of quasitoric manifolds, certain toric orbifolds and a wide family of polyhedral products. This verifies a conjecture of Anick for such spaces. We also describe the additive structure of loop homology of simply connected polyhedral products in terms of polynomials studied by Backelin and Berglund.

Topik & Kata Kunci

math.AT math.AC

Penulis (2)

Lewis Stanton

Fedor Vylegzhanin

Format Sitasi

APA MLA BibTeX

Stanton, L., Vylegzhanin, F. (2025). Anick's conjecture for polyhedral products. https://arxiv.org/abs/2506.15573

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓