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Link Invariants from the Yokonuma–Hecke Algebras Read chapter Read first chapter

2017 | OriginalPaper | Chapter

9. Braid Groups in Handlebodies and Corresponding Hecke Algebras

Author : Valeriy G. Bardakov

Published in: Algebraic Modeling of Topological and Computational Structures and Applications

Publisher: Springer International Publishing

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Abstract

In this paper we study the kernel of the homomorphism \(B_{g,n} \rightarrow B_n\) of the braid group \(B_{g,n}\) in the handlebody \(\mathscr {H}_g\) to the braid group \(B_n\). We prove that this kernel is semi-direct product of free groups. Also, we introduce an algebra \(H_{g,n}(q)\), which is some analog of the Hecke algebra \(H_n(q)\), constructed by the braid group \(B_n\).

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previous chapter Some Hecke-Type Algebras Derived from the Braid Group with Two Fixed Strands
next chapter Infinite Loop Spaces, Dyer–Lashof Algebra, Cohomology of the Infinite Symmetric Group and Modular Invariants
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Metadata
Title
Braid Groups in Handlebodies and Corresponding Hecke Algebras
Author
Valeriy G. Bardakov
Copyright Year
2017
Book
Algebraic Modeling of Topological and Computational Structures and Applications

Print ISBN: 978-3-319-68102-3

Electronic ISBN: 978-3-319-68103-0

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-68103-0_9

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