Algebraic theory of fundamental dimension

Sławomir Nowak

GDML_Books, (1981), p.

Résumé

CONTENTSIntroduction......................................................................................................................................... 5Chapter I Elementary topological characterizations of fundamental dimension........................... 6 1. Characterizations of fundamental dimension..................................................................... 6 2. The fundamental dimension of components of compacta.............................................. 9 3. The fundamental dimension of the union of two compacta............................................. 10Chapter II Cohomology groups over local systems and generalized local systems................... 13 1. Local systems of groups......................................................................................................... 13 2. Cohomology with coefficients in local systems.................................................................. 16 3. The Künneth formula 4. Generalized local systems..................................................................................................... 20Chapter III Homological characterizations of fundamental dimension........................................... 22 1. Deformability of maps and the number................................................................................ 23 2. Obstructions to deformability.................................................................................................. 24 3. Coefficients of cyclicity and ℱ-continua................................................................................. 25 4. Continua with fundamental dimension ≥ 3........................................................................ 28 5. Two algebraic lemmas............................................................................................................ 29 6. Continua with fundamental dimension equal to 1............................................................. 31 7. Continua with fundamental dimension equal to 2............................................................. 33 8. The main results....................................................................................................................... 34Chapter IV Applications of the homological characterizations of fundamental dimensionto the study of some special problems................................................................................................. 37 1. The fundamental dimension of the Cartesian product of a closed manifoldand a continuum........................................................................................................................................ 37 2. The fundamental dimension of the Cartesian product of a curve and a continuum... 38 3. An example of a finite-dimensional continuum with an infinite family of shapefactors and the fundamental dimension of the Cartesian product of polyhedra........................... 42 4. The fundamental dimension of the union of two compacta and of the quotientspace............................................................................................................................................................ 43 5. The fundamental dimension of the suspension of a compactum.................................. 44 6. The fundamental dimension of the Cartesian product of approximative1-connected compacta............................................................................................................................. 46 7. The fundamental dimension of a subset of manifold....................................................... 48Final remarks and problems................................................................................................................... 50References.................................................................................................................................................. 52Index of symbols........................................................................................................................................ 54

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Zbl 0484.55001

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