scholarly journals Rigid hypersurfaces and infinitesimal CR automorphisms

Filomat ◽  
2017 ◽  
Vol 31 (1) ◽  
pp. 77-84
Author(s):  
Atsushi Hayashimoto
Keyword(s):  
Finite Type ◽  
Open Problems ◽  
Infinite Type ◽  
Infinitesimal Cr Automorphisms

We study a survey on the relations between rigid hypersurfaces and infinitesimal CR automorphisms. After reviewing the case of hypersurfaces of finite type, we study the case of hypersurfaces of infinite type. Some open problems are posed in the last section.

scholarly journals Continuous Homomorphisms Defined on (Dense) Submonoids of Products of Topological Monoids

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 23
Author(s):  
Mikhail Tkachenko
Keyword(s):  
Topological Group ◽  
Lie Groups ◽  
Finite Type ◽  
Continuous Homomorphism ◽  
Open Problems ◽  
Group A ◽  
Topological Monoid

We study the factorization properties of continuous homomorphisms defined on a (dense) submonoid S of a Tychonoff product D = ∏ i ∈ I D i of topological or even topologized monoids. In a number of different situations, we establish that every continuous homomorphism f : S → K to a topological monoid (or group) K depends on at most finitely many coordinates. For example, this is the case if S is a subgroup of D and K is a first countable left topological group without small subgroups (i.e., K is an NSS group). A stronger conclusion is valid if S is a finitely retractable submonoid of D and K is a regular quasitopological NSS group of a countable pseudocharacter. In this case, every continuous homomorphism f of S to K has a finite type, which means that f admits a continuous factorization through a finite subproduct of D. A similar conclusion is obtained for continuous homomorphisms of submonoids (or subgroups) of products of topological monoids to Lie groups. Furthermore, we formulate a number of open problems intended to delimit the validity of our results.

scholarly journals Regularity of infinitesimal CR automorphisms

2016 ◽  
Vol 27 (14) ◽  
pp. 1650112 ◽  
Author(s):  
Stefan Fürdös ◽  
Bernhard Lamel
Keyword(s):  
Infinite Type ◽  
Cr Structure ◽  
Cr Structures ◽  
Infinitesimal Cr Automorphisms ◽  
Infinitesimal Automorphisms

We study the regularity of infinitesimal CR automorphisms of abstract CR structures which possess a certain microlocal extension and show that there are smooth multipliers, completely determined by the CR structure, such that if [Formula: see text] is such an infinitesimal CR automorphism, then [Formula: see text] is smooth for all multipliers [Formula: see text]. As an application, we study the regularity of infinitesimal automorphisms of certain infinite type hypersurfaces in [Formula: see text].

scholarly journals BIG MAPPING CLASS GROUPS WITH HYPERBOLIC ACTIONS: CLASSIFICATION AND APPLICATIONS

2021 ◽  
pp. 1-32
Author(s):  
Camille Horbez ◽  
Yulan Qing ◽  
Kasra Rafi
Keyword(s):  
Finite Type ◽  
Hyperbolic Space ◽  
Mapping Class Groups ◽  
Orientable Surface ◽  
Mapping Class ◽  
Bounded Cohomology ◽  
Class Groups ◽  
Infinite Type ◽  
Continuous Actions ◽  
Free Subgroups

Abstract We address the question of determining which mapping class groups of infinite-type surfaces admit nonelementary continuous actions on hyperbolic spaces. More precisely, let $\Sigma $ be a connected, orientable surface of infinite type with tame endspace whose mapping class group is generated by a coarsely bounded subset. We prove that ${\mathrm {Map}}(\Sigma )$ admits a continuous nonelementary action on a hyperbolic space if and only if $\Sigma $ contains a finite-type subsurface which intersects all its homeomorphic translates. When $\Sigma $ contains such a nondisplaceable subsurface K of finite type, the hyperbolic space we build is constructed from the curve graphs of K and its homeomorphic translates via a construction of Bestvina, Bromberg and Fujiwara. Our construction has several applications: first, the second bounded cohomology of ${\mathrm {Map}}(\Sigma )$ contains an embedded $\ell ^1$ ; second, using work of Dahmani, Guirardel and Osin, we deduce that ${\mathrm {Map}} (\Sigma )$ contains nontrivial normal free subgroups (while it does not if $\Sigma $ has no nondisplaceable subsurface of finite type), has uncountably many quotients and is SQ-universal.

A GEOMETRIC AND ALGEBRAIC DESCRIPTION OF ANNULAR BRAID GROUPS

2002 ◽  
Vol 12 (01n02) ◽  
pp. 85-97 ◽  
Author(s):  
RICHARD P. KENT ◽  
DAVID PEIFER
Keyword(s):  
Finite Type ◽  
Cyclic Group ◽  
Semidirect Product ◽  
Braid Group ◽  
Braid Groups ◽  
Artin Group ◽  
Infinite Cyclic Group ◽  
Coxeter Graph ◽  
Infinite Type ◽  
Algebraic Description

We provide a new presentation for the annular braid group. The annular braid group is known to be isomorphic to the finite type Artin group with Coxeter graph Bn. Using our presentation, we show that the annular braid group is a semidirect product of an infinite cyclic group and the affine Artin group with Coxeter graph Ãn - 1. This provides a new example of an infinite type Artin group which injects into a finite type Artin group. In fact, we show that the affine braid group with Coxeter graph Ãn - 1 injects into the braid group on n + 1 stings. Recently it has been shown that the braid groups are linear, see [3]. Therefore, this shows that the affine braid groups are also linear.

scholarly journals SUPERNILPOTENCE PREVENTS DUALIZABILITY

2013 ◽  
Vol 96 (1) ◽  
pp. 1-24 ◽  
Author(s):  
WOLFRAM BENTZ ◽  
PETER MAYR
Keyword(s):  
Finite Type ◽  
Prime Power ◽  
Prime Power Order ◽  
Theoretic Approach ◽  
Direct Products ◽  
Group Operation ◽  
Infinite Type ◽  
Mal’Cev Algebras ◽  
Nilpotent Algebras ◽  
Curious Property

AbstractWe address the question of the dualizability of nilpotent Mal’cev algebras, showing that nilpotent finite Mal’cev algebras with a nonabelian supernilpotent congruence are inherently nondualizable. In particular, finite nilpotent nonabelian Mal’cev algebras of finite type are nondualizable if they are direct products of algebras of prime power order. We show that these results cannot be generalized to nilpotent algebras by giving an example of a group expansion of infinite type that is nilpotent and nonabelian, but dualizable. To our knowledge this is the first construction of a nonabelian nilpotent dualizable algebra. It has the curious property that all its nonabelian finitary reducts with group operation are nondualizable. We were able to prove dualizability by utilizing a new clone theoretic approach developed by Davey, Pitkethly, and Willard. Our results suggest that supernilpotence plays an important role in characterizing dualizability among Mal’cev algebras.

scholarly journals Some open problems and conjectures on submanifolds of finite type: recent development

2014 ◽  
Vol 45 (1) ◽  
pp. 87-108 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Finite Type ◽  
Detailed Account ◽  
Biharmonic Submanifolds ◽  
Open Problems ◽  
Detailed Survey ◽  
First Results ◽  
Finite Type Submanifolds ◽  
Submanifolds Of Finite Type

Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29]. In 1991, a list of twelve open problems and three conjectures on finite type submanifolds was published in [40]. A detailed survey of the results, up to 1996, on this subject was given by the author in [48]. Recently, the study of finite type submanifolds, in particular, of biharmonic submanifolds, have received a growing attention with many progresses since the beginning of this century. In this article, we provide a detailed account of recent development on the problems and conjectures listed in [40].

scholarly journals The Chaotic Properties of Increasing Gap Shifts

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Nor Syahmina Kamarudin ◽  
Malouh Baloush ◽  
Syahida Che Dzul-Kifli
Keyword(s):  
Finite Type ◽  
Shift Of Finite Type ◽  
Infinite Type ◽  
Topologically Mixing

It is well known that locally everywhere onto, totally transitive, and topologically mixing are equivalent on shift of finite type. It turns out that this relation does not hold true on shift of infinite type. We introduce the increasing gap shift and determine its chaotic properties. The increasing gap shift and the sigma star shift serve as counterexamples to show the relation between the three chaos notions on shift of infinite type.

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