The Meyer function on the handlebody group

Key Findings & Data:This gives a cobounding function of Meyer’s signature cocycle on the mapping class group of a 3-dimensional handlebody, i.e. the handlebody group.

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Conclusion & Impact:As an application, we give a topological interpretation for the generator of the first cohomology group of the hyperelliptic handlebody group.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Domain Parameters

Abstract

We give an explicit formula for the signature of handlebody bundles over the circle in terms of the homological monodromy. This gives a cobounding function of Meyer’s signature cocycle on the mapping class group of a 3-dimensional handlebody, i.e. the handlebody group. As an application, we give a topological interpretation for the generator of the first cohomology group of the hyperelliptic handlebody group.

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Cite This Article

KUNO, Y., SATO, M. (2022). The Meyer function on the handlebody group. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 5, 1520–1533. https://ajindex.com/articles/608785

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