ON CONNECTION BETWEEN SOME PROBLEMS OF HOMOTOPY TOPOLOGY AND COMBINATORIAL GROUP THEORY
Abstract
In this paper we formulate basic notions of homotopy topology, tell on hypothesis of Poincare and formulate D(2)-hypothesis. After that we remind some facts from combinatorial group theory, formulate the problem of gap relation and the problem of minimal normal generation. We mention connection between problems of this theory and problems of homotopy topology. In particular, it will be given a reformulation of Poincare's hypothesis in group terms and mention a connection between the problem of gap relation and the D'(2) -hypothesis. Then we offer the method that allows to show for some finite representations of groups that the number ofrelationship can't be reduced (the approach to a problem ofthe minimum normal generation).
About the Authors
Valery Georgievich Bardakov
Novosibirsk State University
Russian Federation
Russian Federation
Michail Vladimirovich Neshchadim
Novosibirsk State University
Russian Federation
Russian Federation
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Review
For citations:
Bardakov V.G., Neshchadim M.V. ON CONNECTION BETWEEN SOME PROBLEMS OF HOMOTOPY TOPOLOGY AND COMBINATORIAL GROUP THEORY. The Bulletin of Kemerovo State University. 2011;(3-1):19-34. (In Russ.)
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