On some topological invariants for morphisms defined in homological spheres

Nasreddine Mohamed Benkafadar

Algeria

University of Constantine

Department of Mathematics, Faculty of Sciences, Professor

Boris Danielovich Gel'man

Russian Federation

Voronezh State University

Department of Functional Theory and Geometry, Faculty of Mathematics

Professor

Submitted: 2013-12-23

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Accepted: 2014-10-17

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Published: 2015-01-28

DOI: https://doi.org/10.4995/agt.2015.2057
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Keywords:

Homology, homotopy, topological degree, fixed points

Supporting agencies:

Project supported by CNEPRU No B00920110092 and PNR / ATRST No 8/u250/713. Laboratory M.M.E.R.E. U.M.1 Constantine. Russian FBR grant 11-01 -00382-a.

Abstract:

In the paper one defines topological invariants of type degree for morphisms in the category Top(2) of topological pairs of spaces and continuous single valued maps, which admit homological n-spheres as target and arbitrary topological pairs of spaces as source. The different described degrees are acquired by means homological methods, and are a powerful tool in the root theory. Several existence theorems are obtained for equations with multivalued transformations.
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References:

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English translation: Russian Math. Surveys 35 (1980), 65-143. https://doi.org/10.1070/RM1980v035n01ABEH001548

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N. M Benkafadar and B. D. Gel'man, Generalized local degree for multi-valued mappings, International Journal of Math. Game Theory and Algebra 10, no. 5 (2000), 413-434.

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