Embedding theorems for quasitoric manifolds

TL;DR

This paper improves classical embedding results for smooth manifolds by providing explicit equivariant embeddings of quasitoric manifolds into Euclidean and projective spaces, with effective dimension bounds.

Contribution

It offers new explicit constructions and bounds for equivariant embeddings of quasitoric manifolds based on combinatorial data.

Findings

Explicit equivariant embeddings constructed

Effective bounds on embedding dimensions established

Applicable to quasitoric manifolds described by combinatorial data

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 $(P,\Lambda)$ into Euclidean and complex projective space. This construction provides effective bounds on the dimension of the equivariant embedding.