Transversal theory and rank functions
نویسندگان
چکیده
منابع مشابه
Transversal Theory
1. Introduction. Transversal theory is a branch of combinatorial mathematics which is only just beginning to emerge as a reasonably connected and coherent subject. Whether this is yet rich enough or mature enough to be called a 'theory' may be a matter for debate; indeed, it is by no means certain that this part of mathematics may not finally be classified under some broader, more comprehensive...
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Implementing an idea due to John Baez and James Dolan we define new invariants of Whitney stratified manifolds by considering the homotopy theory of smooth transversal maps. To each Whitney stratified manifold we assign transversal homotopy monoids, one for each natural number. The assignment is functorial for a natural class of maps which we call stratified normal submersions. When the stratif...
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In this paper, we invoke the theory of generalized inverses and the minus partial order on the study of regular matrices over a commutative ring to define rank–function for regular matrices and dimension–function for finitely generated projective modules which are direct summands of a free module. Some properties held by the rank of a matrix and the dimension of a vector space over a field are ...
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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 o...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1977
ISSN: 0022-247X
DOI: 10.1016/0022-247x(77)90271-2