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An upper bound for the pseudoisotopy stable range.

Mathematische annalen·2020
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Monodromy and mapping class groups of 3-dimensional hypersurfaces.

Oscar Randal-Williams1

  • 1Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB UK.

Mathematische Annalen
|January 23, 2025
PubMed
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.
Keywords:
14D0514M1020E2657R1557R50

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Main Results:

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  • 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.