A Note on Degrees of Twisted Alexander Polynomials Ii

Abstract

Abstract. In this short note we discuss degrees of twisted Alexander polynomials and demonstrate an explicit example of a closed 3-manifold which is related to the degree formula due to Friedl, Kim and Kitayama.

Poincaré duality and degrees of twisted Alexander polynomials

“…(3) Theorem 1.4 is optimal in various ways. For example by [Mo11a], there exists a 3-manifold N with boundary, φ ∈ H 1 (N; Z) and an even dimensional representation α such that the formula in Theorem 1.4 does not hold modulo four. By [Mo11b] similar examples also exist in the closed case.…”