scholarly journals Two Preserver Problems on Induced Maps

2015 ◽  
Vol 05 (05) ◽  
pp. 247-254
Author(s):  
盼盼 闫
Keyword(s):  
Preserver Problems ◽  
Induced Maps

scholarly journals Homological epimorphisms, homotopy epimorphisms and acyclic maps

2020 ◽  
Vol 32 (6) ◽  
pp. 1395-1406
Author(s):  
Joseph Chuang ◽  
Andrey Lazarev
Keyword(s):  
Wide Class ◽  
Topological Spaces ◽  
Loop Spaces ◽  
Graded Algebras ◽  
Differential Graded Algebras ◽  
Algebraic Description ◽  
Acyclic Map ◽  
Induced Maps

AbstractWe show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces. In the case of a universal acyclic map we obtain, for a wide class of spaces, an explicit algebraic description for these induced maps in terms of derived localization.

A note on semi-open and almost open induced maps

2021 ◽  
pp. 107823
Author(s):  
Alvaro Andrade ◽  
Javier Camargo
Keyword(s):  
Almost Open ◽  
Induced Maps

scholarly journals Monotone maps on dendrites and their induced maps

2016 ◽  
Vol 204 ◽  
pp. 121-134 ◽  
Author(s):  
Haithem Abouda ◽  
Issam Naghmouchi
Keyword(s):  
Monotone Maps ◽  
Induced Maps

Lightness of Induced Maps and Homeomorphisms

2011 ◽  
Vol 54 (4) ◽  
pp. 607-618 ◽  
Author(s):  
Javier Camargo
Keyword(s):  
Positive Integer ◽  
Negative Answer ◽  
Arcwise Connected ◽  
Induced Maps

AbstractAn example is given of a map f defined between arcwise connected continua such that C(f) is light and 2f is not light, giving a negative answer to a question of Charatonik and Charatonik. Furthermore, given a positive integer n, we study when the lightness of the induced map 2f or Cn(f) implies that f is a homeomorphism. Finally, we show a result in relation with the lightness of C(C(f)).

scholarly journals Smale endomorphisms over graph-directed Markov systems

2020 ◽  
pp. 1-34
Author(s):  
EUGEN MIHAILESCU ◽  
MARIUSZ URBAŃSKI
Keyword(s):  
Equilibrium Measure ◽  
Parabolic Systems ◽  
Skew Product ◽  
Pointwise Dimension ◽  
Markov Systems ◽  
Large Classes ◽  
Equilibrium Measures ◽  
Skew Products ◽  
Natural Extensions ◽  
Induced Maps

We study Smale skew product endomorphisms (introduced in Mihailescu and Urbański [Skew product Smale endomorphisms over countable shifts of finite type. Ergod. Th. & Dynam. Sys. doi: 10.1017/etds.2019.31. Published online June 2019]) now over countable graph-directed Markov systems, and we prove the exact dimensionality of conditional measures in fibers, and then the global exact dimensionality of the equilibrium measure itself. Our results apply to large classes of systems and have many applications. They apply, for instance, to natural extensions of graph-directed Markov systems. Another application is to skew products over parabolic systems. We also give applications in ergodic number theory, for example to the continued fraction expansion, and the backward fraction expansion. In the end we obtain a general formula for the Hausdorff (and pointwise) dimension of equilibrium measures with respect to the induced maps of natural extensions ${\mathcal{T}}_{\unicode[STIX]{x1D6FD}}$ of $\unicode[STIX]{x1D6FD}$ -maps $T_{\unicode[STIX]{x1D6FD}}$ , for arbitrary $\unicode[STIX]{x1D6FD}>1$ .

scholarly journals Torsion in kernels of induced maps on divisor class groups

2015 ◽  
Vol 14 (08) ◽  
pp. 1550123
Author(s):  
Sean Sather-Wagstaff ◽  
Sandra Spiroff
Keyword(s):  
Projective Dimension ◽  
Class Groups ◽  
Divisor Class ◽  
Finite Projective Dimension ◽  
Induced Maps

We investigate torsion elements in the kernel of the map on divisor class groups of excellent local normal domains A and A/I, for an ideal I of finite projective dimension. The motivation for this work is a result of Griffith–Weston which applies when I is principal.

Sign in / Sign up

Export Citation Format

Share Document