5065

4762

كارشناسي ارشد

هندسه

اصفهان: دانشگاه صنعتي اصفهان،دانشكده علوم رياضي

1388

[هشت]،83ص.:مصور

ص.ع.به فارسي و انگليسي

اعظم اعتماد

عاطفه قرباني

88/12/9

رضا ميرزايي،رسول نصراصفهاني

رياضي

ID4762

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

On the fundamental groups of one dimensional spaces Hanieh Moghadasi h moghadasi@math iut ac ir November 02 2009 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Azam Etemad ae110mat@cc iut ac ir2000 MSC Primary 54F50 Secondary 57M07 57M05Key words Homotopically Hausdor Fundamental group Dendrite Homology Extended commutatorsubgroup In nite multiplication Abstract We study here a number of questions raised by examining the fundamental groups ofcomplicated one dimensional spaces For example we prove that the fundamental group ofa separable connected locally path connected one dimensional metric space is free if andonly if it is countable if and only if the space has a universal cover Among the results we prove are the theorem that states for a separable locally path connectedmetric space X 1 Any free abelian fartor group of X is countable consequently any free factor group of X has countable rank 2 If X is compact then any free abelian factor group of X is nitely generated inconsequently any free factor group of X has nite rank 3 If X is free abelian then X has a universal cover We give examples of one dimensional spaces with interesting fundamental groups general one dimensional spaces have complicated homotopy structure For instance theHawaiian earring which is de ned to be the union of planar circles of radius 1 n for n N tangent to the x axis and passing through the origin The fundamental group of thisrelatively simple compact one dimensional space is not a free group and incidentally is notcountable The main tools which we use are an artinian property and the theory of nerves of covers Thestudy of the relationships between fundamental groups and nerves is particularly relevant tothe study of one dimensional spaces since one dimensionality is a property of nerves and is in fact de ned as such To understand the homotopy groups of spaces which are not semilocally simply connected onemust realize that in such spaces the fundamental group enjoys an in nite product structure We also introduce the notion of as space being homotopically hausdor This key propertyallows us to e ectively study one dimensional spaces but is also enjoyed by many locallysimple spaces such as manifolds and CW complexes 1

اعظم اعتماد

عاطفه قرباني

رضا ميرزايي،رسول نصراصفهاني