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Fixed Points of n-Valued Multimaps of the Circle

Robert F. Brown (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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...

Fixed points of set-valued maps with closed proximally ∞-connected values

Grzegorz Gabor (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Introduction Many authors have developed the topological degree theory and the fixed point theory for set-valued maps using homological techniques (see for example [19, 28, 27, 16]). Lately, an elementary technique of single-valued approximation (on the graph) (see [11, 1, 13, 5, 9, 2, 6, 7]) has been used in constructing the fixed point index for set-valued maps with compact values (see [21, 20, 4]). In [20, 4] authors consider set-valued upper semicontinuous...

Fixed points on Klein bottle fiber bundles over the circle

D. L. Gonçalves, D. Penteado, J. P. Vieira (2009)

Fundamenta Mathematicae

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S¹ for spaces which are fiber bundles over S¹ and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S¹ has been solved recently.

Fixed points on torus fiber bundles over the circle

D. L. Gonçalves, D. Penteado, J. P. Vieira (2004)

Fundamenta Mathematicae

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S¹ for spaces which are fibrations over S¹ and the fiber is the torus ,T. For the case where the fiber is a surface with nonpositive Euler characteristic, we establish general algebraic conditions, in terms of the fundamental group and the induced homomorphism, for the existence of a deformation of a map over S¹ to a fixed point free map. For the case where the fiber is a torus, we classify all maps over...

Foliated groupoids

Lisiecki, Krzysztof (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] The author defines a general notion of a foliated groupoid over a foliation with singularities, within the framework of a (known) general notion of a differentiable structure. Then, he generalizes the classical correspondence between the subalgebras of Lie algebras and the subgroups of the corresponding Lie groups for this type of pseudogroups.

Foncteurs de division et structure de I ⊗ 2 ⊗ Λ n dans la catégorie ℱ

Aurélien Djament (2007)

Annales de l’institut Fourier

Nous démontrons que dans la catégorie ℱ des foncteurs entre espaces vectoriels sur 𝔽 2 , le produit tensoriel entre le second foncteur injectif standard non constant V ↦ 𝔽 2 ( V * ) ⊕ 2 et un foncteur puissance extérieure est artinien. Seul était antérieurement connu le caractère artinien de cet injectif ; notre résultat constitue une étape pour l’étude du troisième foncteur injectif standard non constant de  ℱ .Nous utilisons le foncteur de division par le foncteur identité et des considérations issues de la théorie...

Foncteurs polynomiaux et foncteurs de Mackey non linéaires

Hans-Joachim Baues, Winfried Dreckmann, Vincent Franjou, Teimuraz Pirashvili (2001)

Bulletin de la Société Mathématique de France

On décrit les foncteurs polynomiaux, des groupes abéliens libres vers les groupes abéliens, comme des diagrammes de groupes abéliens dont on explicite les relations.

Foreword

Bureš, J., Souček, V. (1990)

Proceedings of the Winter School "Geometry and Physics"

Formality and the Lefschetz property in symplectic and cosymplectic geometry

Giovanni Bazzoni, Marisa Fernández, Vicente Muñoz (2015)

Complex Manifolds

We review topological properties of Kähler and symplectic manifolds, and of their odd-dimensional counterparts, coKähler and cosymplectic manifolds. We focus on formality, Lefschetz property and parity of Betti numbers, also distinguishing the simply-connected case (in the Kähler/symplectic situation) and the b1 = 1 case (in the coKähler/cosymplectic situation).

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