Displaying similar documents to “The Nielsen coincidence theory on topological manifolds”

Nielsen theory of transversal fixed point sets (with an appendix: C ∞ and C0 fixed point sets are the same, by R. E. Greene)

Helga Schirmer (1992)

Fundamenta Mathematicae

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Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of...

The semi-index product formula

Jerzy Jezierski (1992)

Fundamenta Mathematicae

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We consider fibre bundle maps (...) where all spaces involved are smooth closed manifolds (with no orientability assumption). We find a necessary and sufficient condition for the formula    |ind|(f,g:A) = |ind| (f̅,g̅: p(A)) |ind| ( f b , g b : p - 1 ( b ) ∩ A ) to hold, where A stands for a Nielsen class of (f,g), b ∈ p(A) and |ind| denotes the coincidence semi-index from [DJ]. This formula enables us to derive a relation between the Nielsen numbers N(f,g), N(f̅,g̅) and N ( f b , g b ) .

Homotopical dynamics.

Marzantowicz, Wacław (2003)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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On the generalized Massey–Rolfsen invariant for link maps

A. Skopenkov (2000)

Fundamenta Mathematicae

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For K = K 1 ⊔ . . . ⊔ K s and a link map f : K → ℝ m let K ∼ = ⊔ i < j K i × K j , define a map f ∼ : K ∼ → S m - 1 by f ∼ ( x , y ) = ( f x - f y ) / | f x - f y | and a (generalized) Massey-Rolfsen invariant α ( f ) ∈ π m - 1 ( K ) to be the homotopy class of f ∼ . We prove that for a polyhedron K of dimension ≤ m - 2 under certain (weakened metastable) dimension restrictions, α is an onto or a 1 - 1 map from the set of link maps f : K → ℝ m up to link concordance to π m - 1 ( K ∼ ) . If K 1 , . . . , K s are closed highly homologically connected manifolds of dimension p 1 , . . . , p s (in particular, homology spheres), then π m - 1 ( K ∼ ) ≅ ⊕ i < j π p i + p j - m + 1 S .