Abstract
©2015 Mathematical Sciences Publishers. Let Γ be the fundamental group of the exterior of a knot in the three-sphere. We study deformations of representations of 0 into SLn(C) which are the sum of two irreducible representations. For such representations we give a necessary condition, in terms of the twisted Alexander polynomial, for the existence of irreducible deformations. We also give a more restrictive sufficient condition for the existence of irreducible deformations. We also prove a duality theorem for twisted Alexander polynomials and we describe the local structure of the representation and character varieties.
Original language | English |
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Pages (from-to) | 313-354 |
Journal | Pacific Journal of Mathematics |
Volume | 277 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jan 2015 |
Keywords
- Character variety
- Deformations
- Twisted Alexander polynomial
- Variety of representations