simple connectedness
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Author(s):  
Piotr Malicki

AbstractWe study the simple connectedness of the class of finite-dimensional algebras over an algebraically closed field for which the Auslander–Reiten quiver admits a separating family of almost cyclic coherent components. We show that a tame algebra in this class is simply connected if and only if its first Hochschild cohomology space vanishes.



Author(s):  
Piotr Malicki

AbstractWe study the strong simple connectedness of finite-dimensional tame algebras over an algebraically closed field, for which the Auslander–Reiten quiver admits a separating family of almost cyclic coherent components. As the main application we describe all analytically rigid algebras in this class.



Author(s):  
Raymond Mortini ◽  
Rudolf Rupp
Keyword(s):  


2019 ◽  
Vol 2019 (753) ◽  
pp. 211-237
Author(s):  
Andrea Mondino ◽  
Guofang Wei

AbstractThe main goal of the paper is to prove the existence of the universal cover for {\mathsf{RCD}^{*}(K,N)}-spaces. This generalizes earlier work of [43, 44] on the existence of universal covers for Ricci limit spaces. As a result, we also obtain several structure results on the (revised) fundamental group of {\mathsf{RCD}^{*}(K,N)}-spaces. These are the first topological results for {\mathsf{RCD}^{*}(K,N)}-spaces without extra structural-topological assumptions (such as semi-local simple connectedness).



2019 ◽  
Vol 295 (1-2) ◽  
pp. 341-348
Author(s):  
Osamu Fujino ◽  
Wenfei Liu


2017 ◽  
Vol 18 (2) ◽  
pp. 293-327 ◽  
Author(s):  
Yi Zhu

By studying the theory of rational curves, we introduce a notion of rational simple connectedness for projective homogeneous spaces. As an application, we prove that over a function field of an algebraic surface over an algebraically closed field, a variety whose geometric generic fiber is a projective homogeneous space admits a rational point if and only if the elementary obstruction vanishes.



2015 ◽  
Vol 22 (04) ◽  
pp. 639-654
Author(s):  
Hailou Yao ◽  
Guoqiang Han

Let A be a connected minimal representation-infinite algebra over an algebraically closed field k. In this paper, we investigate the simple connectedness and strong simple connectedness of A. We prove that A is simply connected if and only if its first Hochschild cohomology group H1(A) is trivial. We also give some equivalent conditions of strong simple connectedness of an algebra A.



2015 ◽  
Vol 23 ◽  
pp. 70
Author(s):  
A.M. Pas'ko

The spaces $\mathbb{C}{\Omega}_n$ have been defined. It has been established that the spaces $\mathbb{C}{\Omega}_n$, $n \geqslant 2$ are simply connected.



2015 ◽  
Vol 2015 (699) ◽  
pp. 1-33 ◽  
Author(s):  
Matt DeLand

AbstractRational connectedness is an algebro-geometric analogue of path connectedness depending crucially on the existence of special rational curves called



Author(s):  
Yves Balasko

This chapter addresses the global structure of the equilibrium manifold E. It starts by motivating these global properties for their economic interest. These global properties can be of a topological nature like pathconnectedness, simple connectedness, and contractibility. They can also take a more practical form like the existence of global coordinate systems for the points of the equilibrium manifold in the same way the points at the surface of the earth can be located through their longitude and latitude. The chapter identifies an important subset of the equilibrium manifold, the set of no-trade equilibria. This enables us to uncover the remarkable structure of the equilibrium manifold as a collection of linear spaces parameterized by the no-trade equilibria. This remarkable structure is then applied to define a global coordinate system for the equilibrium manifold.



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