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Lefschetz coincidence formula on non-orientable manifolds

Daciberg Gonçalves, Jerzy Jezierski (1997)

Fundamenta Mathematicae

We generalize the Lefschetz coincidence theorem to non-oriented manifolds. We use (co-) homology groups with local coefficients. This generalization requires the assumption that one of the considered maps is orientation true.

Lefschetz coincidence numbers of solvmanifolds with Mostow conditions

Hisashi Kasuya (2014)

Archivum Mathematicum

For any two continuous maps f , g between two solvmanifolds of the same dimension satisfying the Mostow condition, we give a technique of computation of the Lefschetz coincidence number of f , g . This result is an extension of the result of Ha, Lee and Penninckx for completely solvable case.

Linking and coincidence invariants

Ulrich Koschorke (2004)

Fundamenta Mathematicae

Given a link map f into a manifold of the form Q = N × ℝ, when can it be deformed to an “unlinked” position (in some sense, e.g. where its components map to disjoint ℝ-levels)? Using the language of normal bordism theory as well as the path space approach of Hatcher and Quinn we define obstructions ω ̃ ε ( f ) , ε = + or ε = -, which often answer this question completely and which, in addition, turn out to distinguish a great number of different link homotopy classes. In certain cases they even allow a complete...

Local cohomological properties of homogeneous ANR compacta

V. Valov (2016)

Fundamenta Mathematicae

In accordance with the Bing-Borsuk conjecture, we show that if X is an n-dimensional homogeneous metric ANR continuum and x ∈ X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of Ū and bd U are similar to the properties of the closed ball ⁿ ⊂ ℝⁿ and its boundary n - 1 . We also prove that a metric ANR compactum X of dimension n is dimensionally full-valued if and only if the group Hₙ(X,X∖x;ℤ) is not trivial for some x ∈ X. This implies that...

Locally admissible multi-valued maps

Mirosław Ślosarski (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we generalize the class of admissible mappings as due by L. Górniewicz in 1976. Namely we define the notion of locally admissible mappings. Some properties and applications to the fixed point problem are presented.

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