Fixed Points of n-Valued Multimaps of the Circle

• Autorzy: Robert F. Brown
• Języki publikacji: EN

Abstrakty

EN

A multifunction ϕ: X ⊸ Y is n-valued if ϕ(x) is an unordered subset of n points of Y for each x ∈ X. The (continuous) n-valued multimaps ϕ: S¹ ⊸ S¹ are classified up to homotopy by an integer-valued degree. In the Nielsen fixed point theory of such multimaps, due to Schirmer, the Nielsen number N(ϕ) of an n-valued ϕ: S¹ ⊸ S¹ of degree d equals |n - d| and ϕ is homotopic to an n-valued power map that has exactly |n - d| fixed points. Thus the Wecken property, that Schirmer established for manifolds of dimension at least three, also holds for the circle. An n-valued multimap ϕ: S¹ ⊸ S¹ of degree d splits into n selfmaps of S¹ if and only if d is a multiple of n.

Kategorie tematyczne

• 55M20: Fixed points and coincidences
• 55M25: Degree, winding number
• 54C60: Set-valued maps

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2006
• Tom: 54
• Numer: 2
• Strony: 153-162

Daty

wydano

2006

Twórcy

autor

Robert F. Brown

• Department of Mathematics, University of California, Los Angeles, CA 90095-1555, U.S.A.

Identyfikatory

DOI

10.4064/ba54-2-7