X.S. Lin’s original definition of twisted Alexander knot polynomial is generalized for arbitrary finitely presented groups. J. Cha’s fibering obstruction theorem is generalized. The group of a nontrivial virtual knot shown by L. Kauffman to have trivial Jones polynomial is seen also to have a faithful representation that yields a trivial twisted Alexander polynomial.

In this paper, we give some necessary and sufficient conditions for a normal subgroup of an amalgamated product of groups to be finitely generated. We apply these conditions together with Stallings’ fibering theorem to prove that an irreducible multilink in a homology 3-sphere fibers if and only if each of its multilink splice components fibers.

A p-Laplacian system with Dirichlet boundary conditions is investigated. By analysis of the relationship between the Nehari manifold and fibering maps, we will show how the Nehari manifold changes as λ,μ varies and try to establish the existence of multiple positive solutions. c © 2007 Elsevier Ltd. All rights reserved.

Using recently developed Seifert fibering operators for 3D $\mathcal{N} = 2$ gauge theories, we formulate the necessary ingredients a state-integral model of topological quantum field theory dual to given manifold under 3D-3D correspondence, focusing on case homology spheres with positive orbifold Euler characteristic. We further exhibit set difference that annihilate wavefunctions this TQFT hy...

In this paper we study quasilinear elliptic equations driven by the double phase operator along with a reaction that has singular and parametric superlinear term nonlinear Neumann boundary condition of critical growth. Based on new equivalent norm for Musielak-Orlicz Sobolev spaces Nehari manifold fibering method prove existence at least two weak solutions provided parameter is sufficiently sma...