Loop homology of moment-angle complexes in the flag case
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915691827822592 |
|---|---|
| author | Vylegzhanin, Fedor |
| author_facet | Vylegzhanin, Fedor |
| contents | We develop a general homological approach to presentations of connected graded associative algebras, and apply it to the 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 $H_*(ΩZ_K)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Loop homology of moment-angle complexes in the flag case Vylegzhanin, Fedor Algebraic Topology Combinatorics K-Theory and Homology Rings and Algebras 57S12, 16W50, 16E30 (Primary) 55Q52, 55P35, 55U15, 57T05 (Secondary) We develop a general homological approach to presentations of connected graded associative algebras, and apply it to the 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 $H_*(ΩZ_K)$ 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. |
| title | Loop homology of moment-angle complexes in the flag case |
| topic | Algebraic Topology Combinatorics K-Theory and Homology Rings and Algebras 57S12, 16W50, 16E30 (Primary) 55Q52, 55P35, 55U15, 57T05 (Secondary) |
| url | https://arxiv.org/abs/2403.18450 |