کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5778945 | 1413745 | 2017 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Growth and homogeneity of matchbox manifolds
ترجمه فارسی عنوان
رشد و همگنی چندبعدی کیک بوکسینگ
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
A matchbox manifold with one-dimensional leaves which has equicontinuous holonomy dynamics must be a homogeneous space, and so must be homeomorphic to a classical Vietoris solenoid. In this work, we consider the problem, what can be said about a matchbox manifold with equicontinuous holonomy dynamics, and all of whose leaves have at most polynomial growth type? We show that such a space must have a finite covering for which the global holonomy group of its foliation is nilpotent. As a consequence, we show that if the growth type of the leaves is polynomial of degree at most 3, then there exists a finite covering which is homogeneous. If the growth type of the leaves is polynomial of degree at least 4, then there are additional obstructions to homogeneity, which arise from the structure of nilpotent groups.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Indagationes Mathematicae - Volume 28, Issue 1, February 2017, Pages 145-169
Journal: Indagationes Mathematicae - Volume 28, Issue 1, February 2017, Pages 145-169
نویسندگان
Jessica Dyer, Steven Hurder, Olga Lukina,