56 research outputs found
Dwyer-Kan homotopy theory of enriched categories
We construct a model structure on the category of small categories enriched
over a combinatorial closed symmetric monoidal model category satisfying the
monoid axiom. Weak equivalences are Dwyer-Kan equivalences, i.e. enriched
functors which induce weak equivalences on morphism objects and equivalences of
ordinary categories when we take sets of connected components on morphism
objects.Comment: 39 pages, corrected versio
A note on the converse of the Lefschetz theorem for G-maps
The purpose of this note is to prove the converse of the Lefschetz fixed point theorem (CLT) together with an equivariant version of the converse of the Lefschetz deformation theorem (CDT) in the category of finite G-simplicial complexes, where G is a finite group
The Conley index in Hilbert spaces and its applications
We present a generalization of the classical Conley index defined for flows on locally compact spaces to flows on an infinite-dimensional real Hilbert space H generated by vector fields of the form f: H → H, f(x) = Lx + K(x), where L: H → H is a bounded linear operator satisfying some technical assumptions and K is a completely continuous perturbation. Simple examples are presented to show how this new invariant can be applied in searching critical points of strongly indefinite functionals having asymptotically linear gradient
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