9 papers
On the Uniqueness of the -Equivariant Spectral Flow
Marek Izydorek, Joanna Janczewska, Maciej Starostka +1
The spectral flow is an integer-valued homotopy invariant for paths of selfadjoint Fredholm operators. Lesch as well as Pejsachowicz, Fitzpatrick and Ciriza independently showed th…
Local and Global Bifurcation for Periodic Solutions of Hamiltonian Systems via Comparison Theory for the Spectral Flow
Joanna Janczewska, Maciej Starostka, Nils Waterstraat
We obtain local and global bifurcation for periodic solutions of Hamiltonian systems by using a new way to apply a comparison principle of the spectral flow that was originally int…
The Equivariant Spectral Flow and Bifurcation for Functionals with Symmetries -- Part I
Marek Izydorek, Joanna Janczewska, Maciej Starostka +1
We consider bifurcation of critical points from a trivial branch for families of functionals that are invariant under the orthogonal action of a compact Lie group. Based on a recen…
The relative cup-length in local Morse cohomology
Thomas O. Rot, Maciej Starostka, Nils Waterstraat
Local Morse cohomology associates cohomology groups to isolating neighborhoods of gradient flows of Morse functions on (generally non-compact) Riemannian manifolds . We show tha…
On a Comparison Principle and the Uniqueness of Spectral Flow
Maciej Starostka, Nils Waterstraat
The spectral flow is a well-known quantity in spectral theory that measures the variation of spectra about along paths of selfadjoint Fredholm operators. The aim of this work i…
Connected components of the space of proper gradient vector fields
Maciej Starostka
We show that there exist two proper gradient vector fields on which are homotopic in the category of proper maps but not homotopic in the category of proper gradient…
The -cohomological Conley Index, Cup-Lengths and the Arnold Conjecture on
Maciej Starostka, Nils Waterstraat
We give a new proof of the strong Arnold conjecture for -periodic solutions of Hamiltonian systems on tori, that was first shown by C. Conley and E. Zehnder in 1983. Our proof u…
Morse cohomology in a Hilbert space via the Conley Index
Maciej Starostka
Main theorem of this paper states that Floer cohomology groups in a Hilbert space are isomorphic to the cohomological Conley Index. It is also shown that calculating cohomological…
A remark on singular sets of vector bundle morphisms
Maciej Starostka, Nils Waterstraat
If a characteristic class for two vector bundles over the same base space does not coincide, then the bundles are not isomorphic. We give under rather common assumptions a lower bo…