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Connected sum of representations of knot groups

Pohang Mathematics Institute (PMI), Pohang University of Science and Technology, Pohang 790-784, Republic of Korea

https://doi.org/10.1142/S0218216515500200Cited by:1 (Source: Crossref)

Abstract

When two boundary-parabolic representations of knot groups are given, we introduce the connected sum of these representations and show several natural properties including the unique factorization property. Furthermore, the complex volume of the connected sum is the sum of each complex volumes modulo iπ² and the twisted Alexander polynomial of the connected sum is the product of each polynomials with normalization.

Keywords:

AMSC: 57M05, 57M25, 57M27

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