The character variety of one relator groups

Abstract

We consider some families of one relator groups arising as fundamental groups of 3-dimensional manifolds, and calculate their character varieties in SL(2, C). Then we give simple geometrical descriptions of such varieties, and determine the number of their irreducible components. Our paper relates to the work of Baker-Petersen, Qazaqzeh and Morales-Marcén on the character variety of certain classes of one relator groups, but we use different methods based on the concept of palindrome presentations of given groups.

Keywords

• Finitely generated group
• torus link
• torus bundle
• character variety
• SL(2, C) representation
• Kauffman bracket skein module