Homotopy Theory on Singular Complex Algebraic Varieties

Christophe EyralIMPAN Lecture Notes, Vol. 5, IMPAN, Warszawa, 2022, ISBN 978-83-86806-54-6, 216 pp.

About the book: 
This book aims to provide a short introduction to the topology of algebraic varieties, with a special emphasis placed on singular varieties and their homotopy groups. We first discuss the notion of homotopy depth (introduced by A. Grothendieck), and then pass to Lefschetz–Zariski hyperplane section theorems and Zariski–van Kampen theorems, all the time focusing on singular varieties. We also describe fundamental groups of plane curve complements and investigate Zariski–van Kampen type theorems for higher homotopy groups of hypersurface complements.

About the author: 
Christophe Eyral is Professor at the Institute of Mathematics of the Polish Academy of Sciences in Warsaw. His research interests include singularity theory, algebraic geometry and topology, with the main focus on the geometry and topology of complex singularities.

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