Liminal SL2Zp-Characters of Genus-One Two-Bridge Knot Groups
A result in arithmetic topology showing that reducible SL2 representations of certain knot groups sit as limits of irreducible ones (liminal characters) precisely when a prime divides the first homology of an odd cyclic branched cover of the knot. It links the p-adic arithmetic of a genus-one two-bridge knot's covers to the geometry of its SL2 character variety, using the Alexander polynomial, Legendre symbols, and a divisibility property of Lucas-type sequences.
2501.00323
For a genus-one two-bridge knot K (equivalently a double twist knot J(2k,2l)), this paper connects the arithmetic of its cyclic branched covers to deformations of its SL2 representations. An SL2Zp-ch…