Algebraic discrete Morse theory and applications to commutative algebra [Elektronische Ressource] = (Algebraische diskrete Morse-Theorie und Anwendungen in der kommutativen Algebra) / von Michael Jöllenbeck

Algebraic Discrete Morse TheoryandApplications to CommutativeAlgebra(Algebraische Diskrete Morse-Theorie und Anwendungen inder Kommutativen Algebra)Dissertationzur Erlangung des Doktorgradesder Naturwissenschaften (Dr. rer. nat.)vorgelegt demFachbereich Mathematik und Informatikder Philipps-Universit at MarburgvonMichael J ollenbeckaus Marburg/LahnMarburg/Lahn, Januar 2005Vom Fachbereich Mathematik und Informatikder Philipps-Universit at Marburg als Dissertationangenommen am: 25.04.2005Erstgutachter: Professor Dr. Volkmar WelkerZweitgutachter: Dr. Tim R omerTag der mundlic hen Prufung: 09.05.2005ContentsPart 1. Algebraic Discrete Morse Theory and Applications toCommutative AlgebraChapter 1. Introduction 5Chapter 2. Basics from Commutative Algebra 11x1. Free Resolutions of R-Modules 121.1. Cellular 131.2. Hilbert and Poincare-Betti Series 14x2. Examples for Chain Complexes in Commutative Algebra 152.1. Taylor and Scarf Complex 152.2. Poset Resolution for a Monomial Ordered Family 162.3. Koszul Complex 172.4. Bar Resolution 182.5. Acyclic Hochschild Complex 19x3. Eagon Complex and the Golod Property 213.1. The Eagon Resolution 213.2. The Massey Operations and the Golod Property 23Chapter 3. Algebraic Discrete Morse Theory 29x1. Algebraic Discrete Morse Theory 29x2. Proof of Theorem 1.2 32x3. Normalized Bar and Hochschild Resolution via ADMT 41Chapter 4. Free Resolutions of Monomial Ideals 43x1.