dr inż. Maciej Starostka
Employment
Research fields
Social media
Contact
 maciej.starostka@pg.edu.pl
Adiunkt
 Workplace
 Gmach B pokój 610 E
 Phone
 604100597, (58) 347 23 28
Publication showcase

Morse cohomology in a Hilbert space via the Conley index
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 finitedimensional approximations of the vector field. Further directions are discussed.

A remark on singular sets of vector bundle morphisms
If characteristic classes for two vector bundles over the same base space do not coincide, then the bundles are not isomorphic. We give under rather common assumptions a lower bound on the topological dimension of the set of all points in the base over which a morphism between such bundles is not bijective. Moreover, we show that this set is topologically nontrivial.

Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces
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 LSflows. We apply Ecohomology to index pairs of LSflows and obtain...
Obtained scientific degrees/titles

20170622
Obtained science degree
dr Mathematics (Mathematics)Instytut Matematyczny Polskiej Akademii Nauk
seen 354 times