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The Homotopy Index and Partial Differential Equations - Universitext (Paperback)
  • The Homotopy Index and Partial Differential Equations - Universitext (Paperback)
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The Homotopy Index and Partial Differential Equations - Universitext (Paperback)

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£83.50
Paperback 208 Pages / Published: 24/08/1987
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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.

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN: 9783540180678
Number of pages: 208
Weight: 420 g
Dimensions: 244 x 170 x 12 mm
Edition: Softcover reprint of the original 1st ed. 198

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