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Morse theory of gradient flows, conc...

Katz, Gabriel, (1948-)

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Morse theory of gradient flows, concavity and complexity on manifolds with boundary /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Morse theory of gradient flows, concavity and complexity on manifolds with boundary // Gabriel Katz.
作者:	Katz, Gabriel,
出版者:	New Jersey :World Scientific, : c2020.,
面頁冊數:	xvi, 497 p. :ill. ;24 cm.
內容註:	A prelude in 2D : flows in flatland -- Vector fields, Morse stratifications, and gradient spines of 3-folds -- Concavity and complexity of traversing flows on 3-folds -- Deformations of traversing flows in 3D and modifications of gradient spines -- Stratified convexity and concavity of flows on manifolds with boundary -- Traversally generic and versal flows : semi-algebraic models of tangency -- Combinatorics of tangency : the stratified spaces of real polynomials -- Complexity of shadows and traversing flows in terms of the simplicial volume -- The Burnside ring-valued Morse formula for equivariant vector fields.
標題:	Morse theory. -
ISBN:	9789814368759

Morse theory of gradient flows, concavity and complexity on manifolds with boundary /
Katz, Gabriel,1948-

Morse theory of gradient flows, concavity and complexity on manifolds with boundary /Gabriel Katz. - New Jersey :World Scientific,c2020. - xvi, 497 p. :ill. ;24 cm.

Includes bibliographical references.

A prelude in 2D : flows in flatland -- Vector fields, Morse stratifications, and gradient spines of 3-folds -- Concavity and complexity of traversing flows on 3-folds -- Deformations of traversing flows in 3D and modifications of gradient spines -- Stratified convexity and concavity of flows on manifolds with boundary -- Traversally generic and versal flows : semi-algebraic models of tangency -- Combinatorics of tangency : the stratified spaces of real polynomials -- Complexity of shadows and traversing flows in terms of the simplicial volume -- The Burnside ring-valued Morse formula for equivariant vector fields.

"Putting constraints on the nature of the interaction between nonsingular gradient-like fields and the boundary of a smooth compact manifold have profound implications for the topology of the manifold, and this book describes these implications. Along the way, this study extends into the spaces of flow trajectories, their complexity and intricate combinatorics. New invariants of gradient flows, as well as invariants of the underlying manifold are produced, based on the understanding of these structures (on the space of trajectories and on the flow-generated spines). The process leading to a discovery is equally if not more important than the discover itself and in this book, classical singularity theory guides our investigations, and algebraic topology provides the tools."--Provided by publisher.

ISBN: 9789814368759US178.00

LCCN: 2019034329Subjects--Topical Terms:

706169
Morse theory.

LC Class. No.: QA614.7 / .K37 2020

Dewey Class. No.: 514/.72

Morse theory of gradient flows, concavity and complexity on manifolds with boundary /
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300 $a xvi, 497 p. : $b ill. ; $c 24 cm.
504 $a Includes bibliographical references.
505 0 # $a A prelude in 2D : flows in flatland -- Vector fields, Morse stratifications, and gradient spines of 3-folds -- Concavity and complexity of traversing flows on 3-folds -- Deformations of traversing flows in 3D and modifications of gradient spines -- Stratified convexity and concavity of flows on manifolds with boundary -- Traversally generic and versal flows : semi-algebraic models of tangency -- Combinatorics of tangency : the stratified spaces of real polynomials -- Complexity of shadows and traversing flows in terms of the simplicial volume -- The Burnside ring-valued Morse formula for equivariant vector fields.
520 # $a "Putting constraints on the nature of the interaction between nonsingular gradient-like fields and the boundary of a smooth compact manifold have profound implications for the topology of the manifold, and this book describes these implications. Along the way, this study extends into the spaces of flow trajectories, their complexity and intricate combinatorics. New invariants of gradient flows, as well as invariants of the underlying manifold are produced, based on the understanding of these structures (on the space of trajectories and on the flow-generated spines). The process leading to a discovery is equally if not more important than the discover itself and in this book, classical singularity theory guides our investigations, and algebraic topology provides the tools."--Provided by publisher.
650 # 0 $a Morse theory. $3 706169
650 # 0 $a Manifolds (Mathematics) $3 612607
650 # 0 $a Vector fields. $3 705428