A calculation of the Culler-Shalen seminorms associated to small Seifert Dehn fillings (Q2766416)

Let \(M\) be a compact, connected, irreducible, orientable 3-manifold whose boundary is a torus. Let \(R(M)\) (resp. \(X(M)\)) denote the complex affine algebraic variety whose points correspond to representations NEWLINE\[NEWLINE\rho: \pi_1(M)\to \text{SL}(2,\mathbb{C})NEWLINE\]NEWLINE (resp. to characters \(\chi: \pi_1(M)\to \mathbb{C}\) obtained as compositions \(\text{tr}\circ\rho\)).NEWLINENEWLINENEWLINEThe paper studies the properties of a natural regular function defined on \(X(M)\) and obtains topological consequences on \(M\).