On the dimension of Z-sets
Craig R. Guilbault, Carrie J. Tirel
TL;DR
This paper presents a simple proof that the dimension of a Z-set in a finite-dimensional ANR is less than the dimension of the ambient space, which is significant for understanding group boundaries.
Contribution
It provides an elementary alternative to the cohomological proof of the dimension inequality for Z-sets in finite-dimensional ANRs.
Findings
DimA < DimY for Z-sets in finite-dimensional ANRs
Simplified proof method for dimension inequality
Relevance to the study of group boundaries
Abstract
We offer a short and elementary proof that, for a Z-set A in a finite-dimensional ANR Y, dimA<dimY. This result is relevant to the study of group boundaries. The original proof by Bestvina and Mess relied on cohomological dimension theory.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Topological and Geometric Data Analysis · Advanced Combinatorial Mathematics