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Explore the intricate relationship between open book decompositions and contact topology in this 50-minute conference talk presented at ICBS2025. Delve into the fundamental concepts of open book decompositions and discover how they provide a powerful framework for understanding contact structures on 3-manifolds. Learn about the correspondence between contact structures and open book decompositions, examining how these geometric objects encode topological and geometric information about contact manifolds. Investigate the construction techniques for open book decompositions and their applications in classifying contact structures. Analyze the role of binding and page surfaces in determining contact geometric properties, and understand how modifications to open book decompositions affect the underlying contact topology. Gain insights into current research developments in this active area of low-dimensional topology and contact geometry.
