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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.17998 |
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| _version_ | 1866908416421658624 |
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| author | Thandar, Soumyadip |
| author_facet | Thandar, Soumyadip |
| contents | We study diagrams of commutative differential graded algebras (DGAs) over the orbit category $\sO_G$ in the context of equivariant rational homotopy theory. For $G = C_{pq}$ with $p, q$ distinct primes, we give necessary conditions for injectivity. We prove a combination-type result: the equivariant wedge of injective diagrams over $\mathcal{O}_{C_p}$ and $\mathcal{O}_{C_q}$ with retract structure maps yields an injective diagram over $\mathcal{O}_{C_{pq}}$ with a level-wise minimal model. As an application, we construct examples of $C_{pq}$-formal spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17998 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $C_{pq}$-Injective Diagrams and a Combination Theorem for Minimal Models Thandar, Soumyadip Algebraic Topology 55P91, 55P62, 16E45, 18G10 We study diagrams of commutative differential graded algebras (DGAs) over the orbit category $\sO_G$ in the context of equivariant rational homotopy theory. For $G = C_{pq}$ with $p, q$ distinct primes, we give necessary conditions for injectivity. We prove a combination-type result: the equivariant wedge of injective diagrams over $\mathcal{O}_{C_p}$ and $\mathcal{O}_{C_q}$ with retract structure maps yields an injective diagram over $\mathcal{O}_{C_{pq}}$ with a level-wise minimal model. As an application, we construct examples of $C_{pq}$-formal spaces. |
| title | $C_{pq}$-Injective Diagrams and a Combination Theorem for Minimal Models |
| topic | Algebraic Topology 55P91, 55P62, 16E45, 18G10 |
| url | https://arxiv.org/abs/2506.17998 |