Chris Wendl is Professor of Differential Geometry and Global Analysis at Humboldt University of Berlin. He is the author of Holomorphic Curves in Low Dimensions: From Symplectic Ruled Surfaces to Planar Contact Manifolds (2018), and a recent recipient of an ERC Consolidator Grant.

'… a well-written introduction to the subject that is appropriate for advanced graduate students with a background in algebraic topology and some differential geometry.' Chris Seaton, Mathematical Association of America Reviews

• Introduction; 1. Closed holomorphic curves in symplectic 4-manifolds; 2. Intersections, ruled surfaces and contact boundaries; 3. Asymptotics of punctured holomorphic curves; 4. Intersection theory for punctured holomorphic curves; 5. Symplectic fillings of planar contact 3-manifolds; Appendix A. Properties of pseudoholomorphic curves; Appendix B. Local positivity of intersections; Appendix C. A quick survey of Siefring's intersection theory; References; Index.

Chris Wendl is Professor of Differential Geometry and Global Analysis at Humboldt University of Berlin. He is the author of Holomorphic Curves in Low Dimensions: From Symplectic Ruled Surfaces to Planar Contact Manifolds (2018), and a recent recipient of an ERC Consolidator Grant.

'… a well-written introduction to the subject that is appropriate for advanced graduate students with a background in algebraic topology and some differential geometry.' Chris Seaton, Mathematical Association of America Reviews

• Introduction; 1. Closed holomorphic curves in symplectic 4-manifolds; 2. Intersections, ruled surfaces and contact boundaries; 3. Asymptotics of punctured holomorphic curves; 4. Intersection theory for punctured holomorphic curves; 5. Symplectic fillings of planar contact 3-manifolds; Appendix A. Properties of pseudoholomorphic curves; Appendix B. Local positivity of intersections; Appendix C. A quick survey of Siefring's intersection theory; References; Index.

Chris Wendl is Professor of Differential Geometry and Global Analysis at Humboldt University of Berlin. He is the author of Holomorphic Curves in Low Dimensions: From Symplectic Ruled Surfaces to Planar Contact Manifolds (2018), and a recent recipient of an ERC Consolidator Grant.

'… a well-written introduction to the subject that is appropriate for advanced graduate students with a background in algebraic topology and some differential geometry.' Chris Seaton, Mathematical Association of America Reviews

• Introduction; 1. Closed holomorphic curves in symplectic 4-manifolds; 2. Intersections, ruled surfaces and contact boundaries; 3. Asymptotics of punctured holomorphic curves; 4. Intersection theory for punctured holomorphic curves; 5. Symplectic fillings of planar contact 3-manifolds; Appendix A. Properties of pseudoholomorphic curves; Appendix B. Local positivity of intersections; Appendix C. A quick survey of Siefring's intersection theory; References; Index.