Embedding theorems for quasitoric manifolds

2015/06/15 by Victor Matveevich Buchstaber, Buchstaber, Victor, Andrey Kustarev +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1506.04523

openalex publication_date 2015/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The study of embeddings of smooth manifolds into Euclidean and projective spaces has been for a long time an important area in topology. In this paper we obtain improvements of classical results on embeddings of smooth manifolds, focusing on the case of quasitoric manifolds. We give explicit constructions of equivariant embeddings of a quasitoric manifold described by combinatorial data (P,Λ) into Euclidean and complex projective space. This construction provides effective bounds on the dimension of the equivariant embedding.

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