Modification and the cohomology groups of compact solvmanifolds Ⅱ

Daniel Guan; Daniel Guan

doi:10.3934/era.2025042

Electronic Research Archive

2025, Volume 33, Issue 2: 931-937. doi: 10.3934/era.2025042

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Modification and the cohomology groups of compact solvmanifolds Ⅱ

Daniel Guan ^{1,2
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1.
School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
2.
Department of Mathematics, University of California at Riverside, Riverside, CA 92505, USA

Received: 02 September 2024 Revised: 28 December 2024 Accepted: 08 January 2025 Published: 20 February 2025

In this article, we refine the modification theorem for a compact solvmanifold given in 2006 and completely solve the problem of finding the cohomology ring on compact solvmanifolds.
- solvmanifolds,
- cohomology,
- invariant structure,
- homogeneous space,
- product,
- fiber bundles,
- symplectic manifolds,
- splittings,
- prealgebraic group,
- decompositions,
- modification,
- Lie group,
- compact manifolds,
- uniform discrete subgroups,
- locally flat parallelizable manifolds
Citation: Daniel Guan. Modification and the cohomology groups of compact solvmanifolds Ⅱ[J]. Electronic Research Archive, 2025, 33(2): 931-937. doi: 10.3934/era.2025042

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Abstract

In this article, we refine the modification theorem for a compact solvmanifold given in 2006 and completely solve the problem of finding the cohomology ring on compact solvmanifolds.

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