Shape index in metric spaces

• Autorzy: Francisco R. Ruiz del Portal , José M. Salazar
• Języki publikacji: EN

Abstrakty

EN

We extend the shape index, introduced by Robbin and Salamon and Mrozek, to locally defined maps in metric spaces. We show that this index is additive. Thus our construction answers in the affirmative two questions posed by Mrozek in [12]. We also prove that the shape index cannot be arbitrarily complicated: the shapes of q-adic solenoids appear as shape indices in natural modifications of Smale's horseshoes but there is not any compact isolated invariant set for any locally defined map in a locally compact metric ANR whose shape index is the shape of a generalized solenoid. We also show that, for maps defined in locally compact metric ANRs, the shape index can always be computed in the Hilbert cube. Consequently, the shape index is the shape of the inverse limit of a sequence {Pₙ,gₙ} where Pₙ = P is a fixed ANR and gₙ = g: P → P is a fixed bonding map.

Kategorie tematyczne

• 54H20: Topological dynamics
• 54C56: Shape theory
• 37B30: Index theory, Morse-Conley indices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 176
• Numer: 1
• Strony: 47-62

Daty

wydano

2003

Twórcy

autor

Francisco R. Ruiz del Portal

• Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad Complutense de Madrid, Madrid 28040, Spain

autor

José M. Salazar

• Departamento de Matemáticas, Universidad de Alcalá, Alcalá de Henares, Madrid 28871, Spain

Identyfikatory

DOI

10.4064/fm176-1-4