A survey on embeddings of 3-manifolds in definite 4-manifolds

Paolo Aceto; Duncan McCoy; JungHwan Park

A survey on embeddings of 3-manifolds in definite 4-manifolds

Geometric Topology 2024-11-05 v2

Authors: Paolo Aceto , Duncan McCoy , JungHwan Park

Abstract

This article presents a survey on the topic of embedding 3-manifolds in definite 4-manifolds, emphasizing the latest progress in the field. We will focus on the significant role played by Donaldson's diagonalization theorem and the combinatorics of integral lattices in understanding these embeddings. Additionally, the article introduces a new result concerning the embedding of amphichiral lens spaces in negative-definite manifolds.

Keywords

Donaldson diagonalization theorem integral lattices 3-manifold embedding definite 4-manifold amphichiral lens spaces

Cite

@article{arxiv.2407.03692,
  title  = {A survey on embeddings of 3-manifolds in definite 4-manifolds},
  author = {Paolo Aceto and Duncan McCoy and JungHwan Park},
  journal= {arXiv preprint arXiv:2407.03692},
  year   = {2024}
}

Comments

16 pages, 1 figure, final version

A survey on embeddings of 3-manifolds in definite 4-manifolds

Abstract

Keywords

Cite

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