Polynomial invariants for fibered 3-manifolds and Teichmüller geodesics for foliations

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Closed surface bundles of least volume (2010, methodology): “z e2C t 1 z e7Cz e8/ Now by [17], to get the Teichmüller polynomial we simply compute”
Small dilatation mapping classes coming from the simplest hyperbolic braid (2009, background): “ΘL(x, u) = u 2 − u(1 + x+ x−1) + 1 (4) (see [20] p.”
The lower central series and pseudo-Anosov dilatations (2006, methodology): “For example, a construction of McMullen [Mc] can be used to produce a sequence of pseudo-Anosov elements fn ∈ Mod(Sgn), where gn → ∞, each fn has nonorientable foliations, and log(λ(fn)) ≍ 1/gn.”
The Alexander polynomial of a 3-manifold and the Thurston norm on cohomology (2002, unknown): “Fibered faces of the Thurston norm ball are studied via a polynomial invariant in [ 22 ].”
On groups generated by two positive multi-twists: Teichmuller curves and Lehmer's number (2003, background): “Theorem 6.2 is strikingly similar to the main theorem of [43] (see Theorem 8.4) in which McMullen shows that the minimal spectral radius of any essential element in a Coxeter group with respect to Θ is either 1 or else bounded below by λL .”