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tori and a Seifert fibred structure on $$N|\mathcal {T}_N$$. A graph manifold is a connected and closed 3-manifold which admits a graph structure . We introduce some more terminology to help us deal ...
a conjugacy class invariant called the ideal Whitehead graph |${\rm IW}({\varphi})$| of |${\varphi}$| (see Section 2.6 for details). The graph |$IW({\varphi})$| captures essential information about the structure ...
, the shadow of a Thurston geodesic to the curve graph is a reparameterized quasi-geodesic. However, we show that the set of short curves along the two geodesics are not identical. 1. Introduction In [22 ...
Abstract We consider several natural sets of curves associated to a given Teichmüller disc, such as the systole set or cylinder set, and study their coarse geometry inside the curve graph . We prove ...
with their standard Kähler structure . We will obtain the divisors that we need by blowing up the following two basic configurations of immersed complex spheres in $$\mathbb {CP}^2$$: $$3\ell $$ three complex lines ...
}}))$$and$${\rm vol}(N, {\rm Iso}_e \widetilde {\rm SL_2({\mathbb R})})$$are reached. If$$N$$ admits a hyperbolic geometric structure , then$${\mathrm {HV}}(N)$$equals$${\rm vol}_{{{{\bf{H}}}}^3}(N),$$reached by any ...
that |$\varphi$| has at least the cup-length of |$N$| many leafwise fixed points w.r.t. |$N$|, provided that it is the time-1-map of a global Hamiltonian flow whose restriction to |$N$| stays |$C^0$|-close ...
guarantee that the result of the gluing admits (given the geometrization theorem) a hyperbolic structure . Lackenby's conditions, while considerably more permissive than ours, provide only topological ...
. It fixes a point in Pℴ, since otherwise would act freely on Pℴ and have a finite-dimensional classifying space. This means that Φ belongs to some OutS(G). Consider the action of Φ on the quotient graph ...
. Therefore each $$\overline{\Sigma}_i^2$$ has Euler characteristic $$2$$ and contains exactly two fixed points of the $$G$$ action. ■ 4 Weights, GKM- Graphs and the Moment-Angle Complex Let $$\mathcal{O ...
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