The Homotopy Index and Partial Differential Equations - Softcover

Rybakowski, Krzysztof P.

Softcover

ISBN 10: 0387180672 ISBN 13: 9780387180670

Publisher: Springer Verlag, 1987

Synopsis

The homotopy index theory was developed by Charles Conley for two­ sided flows on compact spaces. The homotopy or Conley index, which provides an algebraic-topologi­ cal measure of an isolated invariant set, is defined to be the ho­ motopy type of the quotient space N /N , where is a certain 1 2 1 2 compact pair, called an index pair. Roughly speaking, N1 isolates the invariant set and N2 is the "exit ramp" of N . 1 It is shown that the index is independent of the choice of the in­ dex pair and is invariant under homotopic perturbations of the flow. Moreover, the homotopy index generalizes the Morse index of a nQnde­ generate critical point p with respect to a gradient flow on a com­ pact manifold. In fact if the Morse index of p is k, then the homo­ topy index of the invariant set {p} is Ik - the homotopy type of the pointed k-dimensional unit sphere.

Edition details

• Publisher: Springer Verlag
• Publication date: 1987
• Language: English
• ISBN 10: 0387180672
• ISBN 13: 9780387180670
• Binding: Paperback