Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology
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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 A∞-algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya’s definition of Morse-A∞-categories for closed oriented manifolds involving families of Morse functions. To make A∞-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 results, requiring only a basic grasp of Morse theory. In particular, no advanced algebra skills are required, and the perturbation theory for Morse trajectories is completely self-contained. In addition to its relevance for finite-dimensional Morse homology, this book may be used as a preparation for the study of Fukaya categories in symplectic geometry. It will be of interest to researchers in mathematics (geometry and topology), and to graduate students in mathematics with a basic command of the Morse theory. Hard cover.

Lieferung aus: Deutschland, zzgl. Versandkosten, in stock, Voraussichtlich lieferbar in 5 Tag(en).
Perturbed Gradient Flow Trees and A-algebra Structures in Morse Cohomology. 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 A -algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya's definition of Morse-A -categories for closed oriented manifolds involving families of Morse functions. To make A -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 results, requiring only a basic grasp of Morse theory. In particular, no advanced algebra skills are required, and the perturbation theory for Morse trajectories is completely self-contained. In addition to its relevance for finite-dimensional Morse homology, this book may be used as a preparation for the study of Fukaya categories in symplectic geometry. It will be of interest to researchersin mathematics (geometry... Buch.

Lieferung aus: Vereinigte Staaten von Amerika, Lagernd, zzgl. Versandkosten.
Perturbed-Gradient-Flow-Trees-and-Aa-algebra-Structures-on-Morse-Cochain-Complexes~~Stephan-Mescher, Perturbed Gradient Flow Trees and Aa??-algebra Structures on Morse Cochain Complexes, Hardcover.

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