Conneted sum of representations of knot groups

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 $i{\pi }^2$ and the twisted Alexander polynomial of the connected sum is the product of each polynomials with normalization.

After the publication of this article, serious errors were found. The author wanted to preserve the content of the publication, so he added the errata in the appendix

References in corpus (1)

• Optimistic limits of colored Jones polynomials and complex volumes of hyperbolic links