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

Paolo Aceto; Duncan McCoy; JungHwan Park

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arXiv · 2407.03692

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

Paolo Aceto·Duncan McCoy·JungHwan Park

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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.

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Paolo Aceto, Duncan McCoy, JungHwan Park. 2024-11-04. A survey on embeddings of 3-manifolds in definite 4-manifolds. https://arxiv.org/abs/2407.03692

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