Some embedding problems in 4-dimensional topology

Carfora, Giulia (2026) Some embedding problems in 4-dimensional topology. PhD thesis, University of Glasgow.

Abstract

This thesis consists of two independent parts addressing problems related to smooth embeddings in 4-dimensional manifolds. In the first part, we consider embeddings of 3-dimensional lens spaces in the complex projective plane. Using an obstruction derived by Owens [59] and relying on Donaldson’s Diagonalisation Theorem [16], we obtain a complete classification of lens spaces of Lisca type (2) or (3) [49] that are unobstructed from embedding in CP2. This classification is further refined for lens spaces L(p, q) of Lisca type (2) or (3) with p even, using an obstruction due to Lidman–Moore–Vazquez [47].

In the second part, we consider a real projective plane smoothly embedded in R4 , on which a height function restricts to a Morse function with five critical points. The aim is to generalise the work by Bleiler–Scharlemann [10] and prove that any such embedding of RP2 is standard, using 3-dimensional topological techniques and graphs of intersection. As the scope was not reached, the second part of the thesis presents an account of the approach undertaken.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Supervisor's Name: Owens, Professor Brendan and Wand, Professor Andy
• Date of Award: 2026
• Depositing User: Theses Team
• Unique ID: glathesis:2026-86088
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 26 Jun 2026 15:46
• Last Modified: 26 Jun 2026 15:53
• URI: https://theses.gla.ac.uk/id/eprint/86088