Abstract
In this chapter, we study a chain map introduced by Inoue and Kabaya, and observe its properties and applications. Roughly speaking, the chain map plays a key role to bridge the quandle homology and relative group homology. In Sect. 8.1, we give a review of the original definition of the map, and describe an outline to address the chain map in detail. Next, in Sect. 8.2, we demonstrate a philosophy to bridge between the map and topological applications (in particular, the fundamental 3-class). After that, following the outline and philosophy, we describe concrete applications. To be precise, in Sect. 8.3, we recover the Chern-Simons invariants of hyperbolic links, and in Sect. 8.4, we will reconsider the bilinear cohomology pairings of links.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsAuthor information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 The Author(s)
About this chapter
Cite this chapter
Nosaka, T. (2017). Inoue–Kabaya Chain Map. In: Quandles and Topological Pairs. SpringerBriefs in Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-10-6793-8_8
Download citation
DOI: https://doi.org/10.1007/978-981-10-6793-8_8
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6792-1
Online ISBN: 978-981-10-6793-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)