Monodromy and mapping class groups of 3-dimensional hypersurfaces

TL;DR

This paper investigates the subgroup of the mapping class group of 3-dimensional hypersurfaces in complex projective 4-space, focusing on those diffeomorphisms realizable through monodromy, to understand their structure and properties.

Contribution

It characterizes the monodromy subgroup within the mapping class group of hypersurfaces in 4, providing new insights into their geometric and topological symmetries.

Findings

Identification of the monodromy subgroup structure

Relations between monodromy and diffeomorphisms

Implications for hypersurface symmetry classification

Abstract

We describe the subgroup of the mapping class group of a hypersurface in $\mathbb{CP}^4$ consisting of those diffeomorphisms which can be realised by monodromy.