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You’ve probably heard about Schrödinger’s cat, which famously is trapped in a box with a mechanism that is activated if a radioactive atom decays, releasing radiation. The act of looking in the b...
A colimit decomposition for homotopy algebras in Cat
A colimit decomposition homotopy algebras Cat Category Theory
2012/6/6
Badzioch showed that in the category of simplicial sets each homotopy algebra of a Lawvere theory is weakly equivalent to a strict algebra. In seeking to extend this result to other contexts Rosicky o...
Effective metastability of Halpern iterates in CAT(0) spaces
Proof mining Banach limits metastability nonexpansive mappings CAT(0) spaces
2011/7/16
Abstract: This paper provides an effective uniform rate of metastability (in the sense of Tao) on the strong convergence of Halpern iterations of nonexpansive mappings in CAT(0) spaces. The extraction...
Random groups have fixed points on CAT(0) cube complexes
Random groups fixed points on CAT(0) cube complexes
2010/12/31
We prove that a random group has fixed points when it isometrically acts on a CAT(0) cube complex. We do not assume that the action is simplicial.
The K-theoretic Farrell-Jones conjecture for CAT(0)-groups
Farrell-Jones conjecture algebraic K-theory of group rings
2010/12/31
We prove the K-theoretic Farrell-Jones conjecture with (twisted)coefficients for CAT(0)-groups.
证明了完备CAT(κ)空间中Halpern算法所产生的迭代序列强收敛于非扩张算子的不动点.
We consider the problem of generating all ideals of a poset. It is a long standing open problem, whether or not the ideals of any poset can be generated in constant amortized time, CAT for short. We ...
Cell-Like Equivalences and Boundaries of CAT(0) Groups
Cell-Like Equivalences Boundaries of CAT(0) Groups
2010/11/1
In 2000, Croke and Kleiner showed that a CAT(0) group G can admit more than one boundary. This contrasted with the situation for word hyperbolic groups, where it was well-known that each such group a...
On the local structure and the homology of CAT$(\kappa)$ spaces and euclidean buildings
local structure CAT$(\kappa)$ spaces euclidean buildings
2010/10/25
We prove that every open subset of a euclidean building is a finite dimensional absolute neighborhood retract. This implies in particular that such a set has the homotopy type of a finite dimensional ...