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Monodromy and mapping class groups of 3-dimensional hypersurfaces
1Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB UK.
Mathematische Annalen
|January 23, 2025
Summary
This study identifies a specific subgroup within the mapping class group related to hypersurfaces. It focuses on diffeomorphisms achievable through monodromy in complex algebraic geometry.
Area of Science:
- Complex algebraic geometry
- Topology
- Group theory
Background:
- The mapping class group (MCG) studies the topology of surfaces.
- Hypersurfaces in complex manifolds are fundamental objects of study.
- Monodromy describes how geometric objects change under continuous deformation.
Purpose of the Study:
- To characterize a specific subgroup of the mapping class group for hypersurfaces.
- To investigate the relationship between diffeomorphisms and monodromy in this context.
Main Methods:
- Utilizing concepts from algebraic geometry and differential topology.
- Analyzing the structure of diffeomorphisms on hypersurfaces.
- Relating these diffeomorphisms to monodromy transformations.
Main Results:
- A precise description of the subgroup of diffeomorphisms realizable by monodromy is provided.
- The study establishes a connection between the geometric monodromy and the algebraic structure of the mapping class group.
Conclusions:
- The identified subgroup offers new insights into the interplay between topology and geometry of hypersurfaces.
- This work contributes to understanding the structure of mapping class groups in higher dimensions.
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