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    Wyświetlanie 1-9 z 9
    Tytuł:
    Nielsen theory of transversal fixed point sets (with an appendix: $C^∞$ and $C^0$ fixed point sets are the same, by R. E. Greene)
    Autorzy:
    Schirmer, Helga
    Powiązania:
    https://bibliotekanauki.pl/articles/1214996.pdf
    Data publikacji:
    1992
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    transversally fixed maps
    minimal and arbitrary fixed point sets
    Nielsen fixed point theory
    relative and extension Nielsen numbers
    Opis:
    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 fixed points in cases where continuous map extensions behave differently from smooth ones. In the appendix it is shown that a subset of a smooth manifold can be realized as the fixed point set of a smooth map in a given homotopy class if and only if it can be realized as the fixed point set of a continuous one. A special case of this result is used in a proof of the paper.
    Źródło:
    Fundamenta Mathematicae; 1992, 141, 1; 31-59
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Minimal fixed point sets of relative maps
    Autorzy:
    Zhao, Xue
    Powiązania:
    https://bibliotekanauki.pl/articles/1205182.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    fixed point class
    minimal fixed point set
    relative Nielsen number
    bipartite graph
    matching
    Opis:
    Let f: (X,A) → (X,A) be a self map of a pair of compact polyhedra. It is known that f has at least N(f;X,A) fixed points on X. We give a sufficient and necessary condition for a finite set P (|P| = N(f;X,A)) to be the fixed point set of a map in the relative homotopy class of the given map f. As an application, a new lower bound for the number of fixed points of f on Cl(X-A) is given.
    Źródło:
    Fundamenta Mathematicae; 1999, 162, 2; 163-180
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Computing Reidemeister classes
    Autorzy:
    Ferrario, Davide
    Powiązania:
    https://bibliotekanauki.pl/articles/1205298.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Reidemeister numbers
    fixed point theory
    Nielsen numbers
    Opis:
    In order to compute the Nielsen number N(f) of a self-map f: X → X, some Reidemeister classes in the fundamental group $π_1(X)$ need to be distinguished. In this paper some algebraic results are given which allow distinguishing Reidemeister classes and hence computing the Reidemeister number of some maps. Examples of computations are presented.
    Źródło:
    Fundamenta Mathematicae; 1998, 158, 1; 1-18
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem
    Autorzy:
    Wong, Peter
    Powiązania:
    https://bibliotekanauki.pl/articles/1215078.pdf
    Data publikacji:
    1992
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    fixed points
    coincidences
    roots
    Lefschetz number
    Nielsen number
    Opis:
    Let $f,g:M_1 → M_2$ be maps where $M_1$ and $M_2$ are connected triangulable oriented n-manifolds so that the set of coincidences $C_{f,g}= {x ∈ M_1 | f(x)=g(x)}$ is compact in $M_1$. We define a Nielsen equivalence relation on $C_{f,g}$ and assign the coincidence index to each Nielsen coincidence class. In this note, we show that, for n ≥ 3, if $M_2= \widetilde M_2/K$ where $\widetilde M_2$ is a connected simply connected topological group and K is a discrete subgroup then all the Nielsen coincidence classes of f and g have the same coincidence index. In particular, when $M_1$ and $M_2$ are compact, f and g are deformable to be coincidence free if the Lefschetz coincidence number L(f,g) vanishes.
    Źródło:
    Fundamenta Mathematicae; 1991-1992, 140, 2; 191-196
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Borel partitions of unity and lower Carathéodory multifunctions
    Autorzy:
    Srivastava, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1208394.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Carathéodory functions and multifunctions
    Carathéodory selections
    fixed points
    Opis:
    We prove the existence of Carathéodory selections and representations of a closed convex valued, lower Carathéodory multifunction from a set A in $A(ℰ ⊗ ℬ(X))$ into a separable Banach space Y, where ℰ is a sub-σ-field of the Borel σ-field ℬ(E) of a Polish space E, X is a Polish space and A is the Suslin operation. As applications we obtain random versions of results on extensions of continuous functions and fixed points of multifunctions. Such results are useful in the study of random differential equations and inclusions and in mathematical economics.
      As a key tool we prove that if A is an analytic subset of E × X and if ${U_n : n ∈ w}$ is a sequence of Borel sets in A such that $A=∪_n U_n$ and the section $U_n(e)$ is open in A(e), e ∈ E, n ∈ w, then there exist Borel functions $p_n : A → [0,1]$, n ∈ w, such that for every e ∈ E, ${p_n(e,·) : n ∈ w}$ is a locally Lipschitz partition of unity subordinate to ${U_n(e) : n ∈ w}$.
    Źródło:
    Fundamenta Mathematicae; 1994-1995, 146, 3; 239-249
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hyperconvexity of ℝ-trees
    Autorzy:
    Kirk, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/1205371.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    hyperconvex metric space
    ℝ-tree
    fixed point
    nonexpansive mapping
    Opis:
    It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete ℝ-tree; (ii) M is hyperconvex and has unique metric segments.
    Źródło:
    Fundamenta Mathematicae; 1998, 156, 1; 67-72
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Lefschetz-type coincidence theorem
    Autorzy:
    Saveliev, Peter
    Powiązania:
    https://bibliotekanauki.pl/articles/1205188.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Lefschetz coincidence theory
    Lefschetz number
    coincidence index
    fixed point
    multivalued map
    Opis:
    A Lefschetz-type coincidence theorem for two maps f,g: X → Y from an arbitrary topological space to a manifold is given: $I_{fg} = λ _{fg}$, that is, the coincidence index is equal to the Lefschetz number. It follows that if $λ_{fg} ≠ 0$ then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y Euclidean, f with acyclic fibres. It also implies certain fixed point results for multivalued maps with "point-like" (acyclic) and "sphere-like" values.
    Źródło:
    Fundamenta Mathematicae; 1999, 162, 1; 65-89
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The fixed-point property for deformations of tree-like continua
    Autorzy:
    Hagopian, Charles
    Powiązania:
    https://bibliotekanauki.pl/articles/1205393.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    fixed point
    arc-component
    deformation
    tree-like continuum
    Borsuk ray
    dog-chases-rabbit argument
    Opis:
    Let f be a map of a tree-like continuum M that sends each arc-component of M into itself. We prove that f has a fixed point. Hence every tree-like continuum has the fixed-point property for deformations (maps that are homotopic to the identity). This result answers a question of Bellamy. Our proof resembles an old argument of Brouwer involving uncountably many tangent curves. The curves used by Brouwer were originally defined by Peano. In place of these curves, we use rays that were originally defined by Borsuk.
    Źródło:
    Fundamenta Mathematicae; 1998, 155, 2; 161-176
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Equivariant Bundle Subtraction Theorem and its applications
    Autorzy:
    Morimoto, Masaharu
    Pawałowski, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/1205192.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    equivariant bundle subtraction
    smooth action on disk
    fixed point set
    equivariant normal bundle
    the family of large subgroups of a finite group
    Opis:
    In the theory of transformation groups, it is important to know what kind of isotropy subgroups of G do occur at points of the space upon which the given group G acts. In this article, for a finite group G, we prove the Equivariant Bundle Subtraction Theorem (Theorem 2.2) which allows us to construct smooth G-manifolds with prescribed isotropy subgroups around the G-fixed point sets. In Theorem 0.1, we restate Oliver's result about manifolds M and G-vector bundles over M that occur, respectively, as the G-fixed point sets and their equivariant normal bundles for smooth G-actions on disks. In Theorems 0.2 and 0.3, we prove the corresponding results for smooth G-actions on disks with prescribed isotropy subgroups around M. In Theorems 0.4 and 0.5, for large classes of finite groups G, we explicitly describe manifolds M that occur as the G-fixed point sets for such actions on disks. These actions are expected to be useful for answering the question of which manifolds occur as the G-fixed points sets for smooth G-actions on spheres.
    Źródło:
    Fundamenta Mathematicae; 1999, 161, 3; 279-303
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-9 z 9

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