The universal cover of a representation-finite algebra

1981 ◽  
pp. 68-105 ◽  
Author(s):  
P. Gabriel
Keyword(s):  
Finite Algebra ◽  
Universal Cover

scholarly journals Dynamical incoherence for a large class of partially hyperbolic diffeomorphisms

2020 ◽  
pp. 1-17
Author(s):  
THOMAS BARTHELMÉ ◽  
SERGIO R. FENLEY ◽  
STEVEN FRANKEL ◽  
RAFAEL POTRIE
Keyword(s):  
Large Class ◽  
Universal Cover ◽  
Isotopy Class ◽  
Seifert Manifold ◽  
Hyperbolic Diffeomorphisms ◽  
Surface Homeomorphisms ◽  
Partially Hyperbolic ◽  
Partially Hyperbolic Diffeomorphisms ◽  
Partially Hyperbolic Diffeomorphism

Abstract We show that if a partially hyperbolic diffeomorphism of a Seifert manifold induces a map in the base which has a pseudo-Anosov component then it cannot be dynamically coherent. This extends [C. Bonatti, A. Gogolev, A. Hammerlindl and R. Potrie. Anomalous partially hyperbolic diffeomorphisms III: Abundance and incoherence. Geom. Topol., to appear] to the whole isotopy class. We relate the techniques to the study of certain partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds performed in [T. Barthelmé, S. Fenley, S. Frankel and R. Potrie. Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, part I: The dynamically coherent case. Preprint, 2019, arXiv:1908.06227; Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, part II: Branching foliations. Preprint, 2020, arXiv: 2008.04871]. The appendix reviews some consequences of the Nielsen–Thurston classification of surface homeomorphisms for the dynamics of lifts of such maps to the universal cover.

scholarly journals Characterisation of polyhedral products with finite generalised Postnikov decomposition

2020 ◽  
Vol 32 (5) ◽  
pp. 1253-1269
Author(s):  
Kouyemon Iriye ◽  
Daisuke Kishimoto ◽  
Ran Levi
Keyword(s):  
Finite Length ◽  
Inverse Limit ◽  
Universal Cover ◽  
Homotopy Equivalent ◽  
Polyhedral Product ◽  
Postnikov Tower

AbstractA generalised Postnikov tower for a space X is a tower of principal fibrations with fibres generalised Eilenberg–MacLane spaces, whose inverse limit is weakly homotopy equivalent to X. In this paper we give a characterisation of a polyhedral product {Z_{K}(X,A)} whose universal cover either admits a generalised Postnikov tower of finite length, or is a homotopy retract of a space admitting such a tower. We also include p-local and rational versions of the theorem. We end with a group theoretic application.

scholarly journals Spherical posets from commuting elements

2018 ◽  
Vol 21 (4) ◽  
pp. 593-628 ◽  
Author(s):  
Cihan Okay
Keyword(s):  
Homotopy Type ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Universal Cover ◽  
Homotopy Equivalent ◽  
Classifying Space ◽  
Partially Ordered ◽  
Abelian Subgroups

AbstractIn this paper, we study the homotopy type of the partially ordered set of left cosets of abelian subgroups in an extraspecial p-group. We prove that the universal cover of its nerve is homotopy equivalent to a wedge of r-spheres where {2r\geq 4} is the rank of its Frattini quotient. This determines the homotopy type of the universal cover of the classifying space of transitionally commutative bundles as introduced in [2].

scholarly journals The non-backtracking spectrum of the universal cover of a graph

2014 ◽  
Vol 367 (6) ◽  
pp. 4287-4318 ◽  
Author(s):  
Omer Angel ◽  
Joel Friedman ◽  
Shlomo Hoory
Keyword(s):  
Universal Cover

scholarly journals The universal cover of a quiver with relations

1983 ◽  
Vol 30 (3) ◽  
pp. 277-292 ◽  
Author(s):  
R. Martínez-Villa ◽  
J.A. De la Peña
Keyword(s):  
Universal Cover

scholarly journals A Pair of Rigid Surfaces with pg= q = 2 and K2= 8 Whose Universal Cover is Not the Bidisk

2018 ◽  
Vol 2020 (11) ◽  
pp. 3453-3493
Author(s):  
Francesco Polizzi ◽  
Carlos Rito ◽  
Xavier Roulleau
Keyword(s):  
Minimal Surfaces ◽  
Universal Cover ◽  
The Family ◽  
Albanese Map ◽  
Rigid Surfaces

Abstract We construct two complex-conjugated rigid minimal surfaces with $p_g\!=q=2$ and $K^2\!=8$ whose universal cover is not biholomorphic to the bidisk $\mathbb{H} \times \mathbb{H}$. We show that these are the unique surfaces with these invariants and Albanese map of degree 2, apart from the family of product-quotient surfaces given in [33]. This completes the classification of surfaces with $p_g=q=2, K^2=8$, and Albanese map of degree 2.

scholarly journals A semi-finite algebra associated to a subfactor planar algebra

2011 ◽  
Vol 261 (5) ◽  
pp. 1345-1360 ◽  
Author(s):  
A. Guionnet ◽  
V. Jones ◽  
D. Shlyakhtenko
Keyword(s):  
Finite Algebra ◽  
Planar Algebra
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