The braid group representation on intersection matrices and monodromy of singularities [Elektronische Ressource] / vorgelegt von Gunnar Dietz

Gunnar DietzThe Braid Group Representationon Intersection Matricesand Monodromy of Singularities2005MathematikThe Braid Group Representationon Intersection Matricesand Monodromy of SingularitiesInaugural-Dissertationzur Erlangung des Doktorgradesder Naturwissenschaften im FachbereichMathematik und Informatikder Mathematisch-Naturwissenschaftlichen Fakultätder Westfälischen Wilhelms-Universität Münstervorgelegt vonGunnar Dietzaus Hamburg- 2005 -Dekan: Prof. Dr. Klaus HinrichsErster Gutachter: Prof. Dr. Helmut A. HammZweiter Gutachter: Prof. Dr. Wolfgang EbelingTag der mündlichen Prüfung: 28. September 2005Tag der Promotion: 28. September 2005To Angie and my parentsAbstractAbstract. Itisawell-knownfactthatthemonodromyoftheMilnorfibrationofanisolatedsingularity is quasiunipotent. This holds no longer true if a non-local monodromy aroundseveral singularities is considered. Here the case of families of (finitely many) Morsesingularities will be studied. For the case that such a family arises from a morsificationof an isolated singularity it will be proven that all monodromies corresponding to simpleloops around a subfamily of the corresponding critical values are already quasiunipotentif and only if this is always the case for simple loops around only two critical values. Weconjecture that this is (for purely combinatorial reasons) also true for the general caseand prove a weaker analogon of this conjecture.Zusammenfassung.