scholarly journals Complete gradient shrinking Ricci solitons have finite topological type

2008 ◽  
Vol 346 (11-12) ◽  
pp. 653-656 ◽  
Author(s):  
Fu-quan Fang ◽  
Jian-wen Man ◽  
Zhen-lei Zhang
Keyword(s):  
Topological Type ◽  
Ricci Solitons ◽  
Finite Topological Type

EXHAUSTION OF THE CURVE GRAPH VIA RIGID EXPANSIONS

2018 ◽  
Vol 61 (1) ◽  
pp. 195-230 ◽  
Author(s):  
JESÚS HERNÁNDEZ HERNÁNDEZ
Keyword(s):  
Topological Type ◽  
Orientable Surface ◽  
Finite Topological Type ◽  
Curve Graph ◽  
Finite Set ◽  
Rigid Set

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.

scholarly journals On manifolds with quadratic curvature decay

2009 ◽  
Vol 145 (2) ◽  
pp. 528-540 ◽  
Author(s):  
Nader Yeganefar
Keyword(s):  
Topological Type ◽  
Noncompact Manifold ◽  
Asymptotic Cones ◽  
Finite Topological Type ◽  
Curvature Decay

AbstractWe give conditions which imply that a complete noncompact manifold with quadratic curvature decay has finite topological type. In particular, we find links between the topology of a manifold with quadratic curvature decay and some properties of the asymptotic cones of such a manifold.

scholarly journals FINITE RIGID SETS IN CURVE COMPLEXES

2013 ◽  
Vol 05 (02) ◽  
pp. 183-203 ◽  
Author(s):  
JAVIER ARAMAYONA ◽  
CHRISTOPHER J. LEININGER
Keyword(s):  
Class Group ◽  
Topological Type ◽  
Orientable Surface ◽  
Mapping Class ◽  
Curve Complex ◽  
Finite Topological Type ◽  
Punctured Torus ◽  
Curve Complexes ◽  
Simplicial Map ◽  
Pointwise Stabilizer

We prove that curve complexes of surfaces are finitely rigid: for every orientable surface S of finite topological type, we identify a finite subcomplex 𝔛 of the curve complex [Formula: see text] such that every locally injective simplicial map [Formula: see text] is the restriction of an element of [Formula: see text], unique up to the (finite) pointwise stabilizer of 𝔛 in [Formula: see text]. Furthermore, if S is not a twice-punctured torus, then we can replace [Formula: see text] in this statement with the extended mapping class group Mod ±(S).

Circle patterns on surfaces of finite topological type revisited

2020 ◽  
Vol 306 (1) ◽  
pp. 203-220
Author(s):  
Yue-Ping Jiang ◽  
QiangHua Luo ◽  
Ze Zhou
Keyword(s):  
Topological Type ◽  
Finite Topological Type ◽  
Circle Patterns

On Manifolds with Lower Quadratic Curvature Decay and Volume Pinching

2018 ◽  
Vol 2020 (21) ◽  
pp. 7857-7872
Author(s):  
Xiaosong Kang ◽  
Xu Xu ◽  
Dunmu Zhang
Keyword(s):  
Riemannian Manifold ◽  
Topological Type ◽  
Finite Topological Type ◽  
Noncompact Riemannian Manifold ◽  
Curvature Decay

Abstract We give some conditions for a complete noncompact Riemannian manifold with lower quadratic curvature decay to have finite topological type. Most of our curvature conditions are much weaker than the assumptions in Lott [5] and in Sha–Shen [10], hence our results can be viewed as natural generalizations of those works.

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