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Explore the foundations of homotopy theory in this comprehensive lecture from the "Dualities in Topology and Algebra" online program. Delve into key concepts such as homotopy of maps, CW complexes, homotopy equivalence, fibrations, mapping cylinders, weak equivalence, and the Barratt sequence. Learn how these fundamental ideas contribute to understanding duality phenomena in topology and algebra, and gain insights into their applications in various mathematical fields. This 56-minute presentation by Samik Basu from the International Centre for Theoretical Sciences provides a solid groundwork for further study in algebraic topology and related areas.
