This short book for graduate students presents the essential parts of differential and low-dimensional topology so that the reader may become 'literate' in the field and begin research as quickly as possible, while keeping the prerequisites to a minimum. A novel feature at this level is the inclusion of the modern theory of Heegaard Floer homology.
This short book for graduate students presents the essential parts of differential and low-dimensional topology so that the reader may become 'literate' in the field and begin research as quickly as possible, while keeping the prerequisites to a minimum. A novel feature at this level is the inclusion of the modern theory of Heegaard Floer homology.
András Juhász is Professor of Mathematics at the University of Oxford. He specialises in low-dimensional topology and knot theory from the point of view of invariants such as Heegaard Floer homology. Recently, in collaboration with DeepMind, he has been exploring how machine learning might be used to advance pure mathematics.
Inhaltsangabe
Preface 1. Background on topological and smooth manifolds 2. Higher-dimensional manifolds 3. Three-manifolds 4. Knots and links 5. Heegaard floer homology 6. Four-manifolds Appendix: Fibre bundles and characteristic classes Bibliography Index.