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In this paper, we investigate a family of graphs associated to collections of arcs on surfaces. These {\it multiarc graphs} naturally interpolate between arc graphs and flip graphs, both well studied objects in low dimensional geometry and topology. We show a number of rigidity results, namely showing that, under certain complexity conditions, that simplicial maps between them only arise in the ``obvious way". We also observe that, again under necessary complexity conditions, subsurface strata are convex. Put together, these results imply that certain simplicial maps always give rise to convex images.
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참고문헌 (14)
참고문헌 신청
J. Aramayona / 2010 / Simplicial embeddings between pants graphs / Geom. Dedicata 144:115~128
J. Aramayona / 2015 / Injective maps between ip graphs / Ann. Inst. Fourier (Grenoble) 65(5):2037~2055
J. Aramayona / 2013 / Convexity of strata in diagonal pants graphs of surfaces / Publ. Mat 57(1):219~237
J. Aramayona / 2008 / Totally geodesic subgraphs of the pants complex / Math. Res. Lett 15(2):309~320
J. Aramayona / 2009 / Constructing convex planes in the pants complex / Proc. Amer. Math. Soc 137(10):3523~3531
J. Aramayona / 2015 / Injective maps between ip graphs / Ann. Inst. Fourier (Grenoble) 65(5):2037~2055
J. Aramayona / 2013 / Convexity of strata in diagonal pants graphs of surfaces / Publ. Mat 57(1):219~237
J. Aramayona / 2008 / Totally geodesic subgraphs of the pants complex / Math. Res. Lett 15(2):309~320
J. Aramayona / 2009 / Constructing convex planes in the pants complex / Proc. Amer. Math. Soc 137(10):3523~3531
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