Perturbed Gradient Flow Trees and A8-algebra Structures in Morse Cohomology (eBook, PDF)
Stephan Mescher
eBook, PDF

Perturbed Gradient Flow Trees and A8-algebra Structures in Morse Cohomology (eBook, PDF)

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This book elaborates on an idea put forward by M. Abouzaid on equipping the Morse cochain complex of a smooth Morse function on a closed oriented manifold with the structure of an A8-algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya's definition of Morse-A8-categories for closed oriented manifolds involving families of Morse functions. To make A8-structures in Morse theory accessible to a broader audience, this book provides a coherent and detailed treatment of Abouzaid's approach, including a discussion of all relevant analytic notions and res...

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