High dimensional analogue of metric distortion for simplicial complexes
Izhar Oppenheim
TL;DR
This paper introduces a high-dimensional analogue of metric distortion for simplicial complexes, proposes a method to establish lower bounds, and proves a Bourgain-type distortion theorem for Linial-Meshulam random complexes.
Contribution
It presents a novel high-dimensional distortion concept, a method for lower bounds, and a Bourgain-type theorem for random complexes.
Findings
Established a high-dimensional distortion analogue.
Developed a method for lower bounds on distortion.
Proved a Bourgain-type distortion theorem for Linial-Meshulam complexes.
Abstract
We suggest a new possible high dimensional analogue to metric distortion. We then show a possible method for providing lower bounds to this distortion and use this method to prove a "Bourgain-type" distortion theorem for Linial-Meshulam random complexes.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Point processes and geometric inequalities · Limits and Structures in Graph Theory