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Mathematics > Algebraic Topology
Title: Loop homology of moment-angle complexes in the flag case
(Submitted on 27 Mar 2024 (v1), last revised 4 Apr 2024 (this version, v2))
Abstract: We develop a general homological approach to presentations of connected graded associative algebras, and apply it to loop homology of moment-angle complexes $Z_K$ that correspond to flag simplicial complexes $K$. For arbitrary coefficient ring, we describe generators of the Pontryagin algebra $H_*(\Omega Z_K)$ and defining relations between them. We prove that such moment-angle complexes are coformal over $\mathbb{Q},$ give a necessary condition for rational formality, and compute their homotopy groups in terms of homotopy groups of spheres.
Submission history
From: Fedor Vylegzhanin [view email][v1] Wed, 27 Mar 2024 11:09:27 GMT (37kb,D)
[v2] Thu, 4 Apr 2024 17:34:24 GMT (37kb,D)
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