Search results for: SEIBERG–WITTEN–FLOER HOMOLOGY

• Seiberg-Witten invariants the topological degree and wall crossing formula

  Publication

  • M. Starostka

  - Central European Journal of Mathematics - Year 2012

  Following S. Bauer and M. Furuta we investigate finite dimensional approximations of a monopole map in the case b 1 = 0. We define a certain topological degree which is exactly equal to the Seiberg-Witten invariant. Using homotopy invariance of the topological degree a simple proof of the wall crossing formula is derived.

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• Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces

  Publication

  • M. Izydorek
  • T. O. Rot
  • M. Starostka
  • M. Styborski
  • R. C. Vandervorst

  - JOURNAL OF DIFFERENTIAL EQUATIONS - Year 2017

  In this paper we introduce a new compactness condition — Property-(C) — for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying the this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain...

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• Morse cohomology in a Hilbert space via the Conley index

  Publication

  • M. Starostka

  - Journal of Fixed Point Theory and Applications - Year 2015

  The main theorem of this paper states that Morse cohomology groups in a Hilbert space are isomorphic to the cohomological Conley index. It is also shown that calculating the cohomological Conley index does not require finite-dimensional approximations of the vector field. Further directions are discussed.

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