An obstruction to lens spaces embedding in CP^2

Giulia Carfora (University of Glasgow)

Monday 27th October 15:00-16:00
Maths 311B

Abstract

Smooth embeddings of manifolds into higher dimensional manifolds have been actively studied for many years. In this talk we concentrate on 3-dimensional lens spaces. It is known that they embed into 5-dimensional space, so the interesting question regards embeddings into 4-dimensional manifolds. A homological argument proves that lens spaces in general do not embed into S^4. The next candidate 4-manifold we consider is \mathbb{C}P^2. Using Donaldson's Diagonalization Theorem A, it is possible to derive an obstruction to when a lens space embeds into \mathbb{C}P^2. In this talk we discuss all of the above and provide infinite families of lens spaces which are unobstructed from embedding into \mathbb{C}P^2.

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