Rigidity of the nonseparating and outer curve graph

2018 ◽  
Vol 26 (1) ◽  
pp. 75-97
Author(s):  
Jesús Hernández Hernández
Keyword(s):  
2018 ◽  
Vol 61 (1) ◽  
pp. 195-230 ◽  
Author(s):  
JESÚS HERNÁNDEZ HERNÁNDEZ

AbstractFor an orientable surfaceSof finite topological type with genusg≥ 3, we construct a finite set of curves whose union of iterated rigid expansions is the curve graph$\mathcal{C}$(S). The set constructed, and the method of rigid expansion, are closely related to Aramayona and Leiniger's finite rigid set in Aramayona and Leininger,J. Topology Anal.5(2) (2013), 183–203 and Aramayona and Leininger,Pac. J. Math.282(2) (2016), 257–283, and in fact a consequence of our proof is that Aramayona and Leininger's set also exhausts the curve graph via rigid expansions.


2014 ◽  
Vol 46 (5) ◽  
pp. 989-1002 ◽  
Author(s):  
Tarik Aougab ◽  
Samuel J. Taylor

2016 ◽  
Vol 65 (4) ◽  
pp. 813-832
Author(s):  
Brian Bowditch
Keyword(s):  

2014 ◽  
Vol 24 (02) ◽  
pp. 121-169 ◽  
Author(s):  
Sang-Hyun Kim ◽  
Thomas Koberda

We develop an analogy between right-angled Artin groups and mapping class groups through the geometry of their actions on the extension graph and the curve graph, respectively. The central result in this paper is the fact that each right-angled Artin group acts acylindrically on its extension graph. From this result, we are able to develop a Nielsen–Thurston classification for elements in the right-angled Artin group. Our analogy spans both the algebra regarding subgroups of right-angled Artin groups and mapping class groups, as well as the geometry of the extension graph and the curve graph. On the geometric side, we establish an analogue of Masur and Minsky's Bounded Geodesic Image Theorem and their distance formula.


2021 ◽  
Vol 70 (4) ◽  
pp. 1625-1637
Author(s):  
Hyungryul Baik ◽  
Hyunshik Shin ◽  
Chenxi Wu
Keyword(s):  

Author(s):  
Jacob Russell

Abstract We provide a simple, combinatorial criteria for a hierarchically hyperbolic space to be relatively hyperbolic by proving a new formulation of relative hyperbolicity in terms of hierarchy structures. In the case of clean hierarchically hyperbolic groups, this criteria characterizes relative hyperbolicity. We apply our criteria to graphs associated to surfaces and prove that the separating curve graph of a surface is relatively hyperbolic when the surface has zero or two punctures. We also recover a celebrated theorem of Brock and Masur on the relative hyperbolicity of the Weil–Petersson metric on Teichmüller space for surfaces with complexity three.


2015 ◽  
Vol 8 (4) ◽  
pp. 1085-1118 ◽  
Author(s):  
Anna Lenzhen ◽  
Kasra Rafi ◽  
Jing Tao
Keyword(s):  

1868 ◽  
Vol 5 (51) ◽  
pp. 393-395
Author(s):  
James Geikie

It Will interest some of your readers to hear that remains of Bos primigenius have recently been obtained from the true till or lower Boulder-clay of Scotland. The specimens hitherto found appear to have come either from the fine Glacial brick-clays, which are posterior in date to the larger portion of our Boulder-clay, or from deposits of still later age. A few days ago I heard that the navvies employed in making the new “Crofthead and Kilmarnock Extension Railway” had come upon what was described to me as a “wounderful big bull's head.” I lost no time in visiting the locality, and saw the fossil in the possession of Mr. John Strain, C.E., who allowed me to examine it, and was afterwards kind enough to accompany me to the railway cutting in order to point out the exact spot from which the relic was taken. The skull is in rather an imperfect state, and only one of the horn-cores remains, the other having been broken off near the base. The perfect core measures 31 inches in length along the outer curve, and gives at its base a circumferences of 14 inches. The breadth of the forehead between the horns is 10 inches. From the character of the flat forehead, from the origin of the cores, and from the direction and curvature of the remaining one, there can be no doubt that the skull is that of Bos primigenius.


2021 ◽  
pp. 107730
Author(s):  
Hong Chang ◽  
Xifeng Jin ◽  
William W. Menasco
Keyword(s):  

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