Sparse maps

Elia Portnoy

Sparse maps

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arxiv 2407.05137 v3 pith:BWSA3KG7 submitted 2024-07-06 math.MG

Elia Portnoy This is my paper · ORCID

classification math.MG

keywords mapscomplexessimplicialsparsealongcontrolleddiscusseuclidean

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We prove a generalization of the Kolmogorov-Barzdin theorem for maps from simplicial complexes into Euclidean space. Along the way we introduce the notion of sparse maps and discuss maps from simplicial complexes with controlled 1-waist.

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Milnor invariants and thickness of spherical links
math.GT 2025-09 conditional novelty 7.0 of 10

Higher-dimensional spherical links have Milnor invariants that grow at most polynomially with 1/thickness when a 1-dimensional component is present, and exponentially otherwise; both rates are asymptotically sharp, an...

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