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LECTURES ON OPEN BOOK DECOMPOSITIONS AND

LECTURES ON OPEN BOOK DECOMPOSITIONS AND 2025

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The document presents a comprehensive survey on open book decompositions and contact structures, primarily focusing on Giroux's fundamental theorem which establishes a correspondence between oriented contact structures on closed oriented 3-manifolds and open book decompositions. It discusses the implications of this theorem for studying cobordisms and filling properties of contact structures, along with various applications in topology. The text assumes familiarity with low-dimensional topology and provides detailed proofs, definitions, and examples related to open books, contact structures, and their interrelations. Additionally, it explores symplectic fillings and the relationship between contact geometry and topological properties of manifolds.

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