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Welcome to the website! The lecture is taught by Pavle Blagojević and Holger Reich and is a continuation of Topologie I, taught in the SoSe 2014. . Although it is helpful to have taken Topologie I, it is not necessary. |
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Course Description This course is a continuation of Topologie I, taught last semester. Although it is helpful to have taken Topologie I to follow the present course, it is not (absolutely) necessary. The aim of Topologie II is a skillful handling and thorough understanding of all notions of homology and cohomology including products, the cup and cross product, as well as several types of duality. The course will roughly be structured as follows:
Applications in optimization, number theory, algebra, algebraic geometry, and functional analysis
The course will loosely be based on lecture notes by Milnor (not freely available). We also recommend the books by J. Munkres ("Elements of Algebraic Topology", Addison-Wesley 1984) and A. Hatcher ("Algebraic Topology", Cambridge U Press 2002, also online) and the succinct lecture notes by J. P. May ("A Concise Course in Algebraic Topology", online)The course will use material from P. M. Gruber, " Convex and Discrete Geometry" (Springer 2007) and various other sources. There will be brief lecture notes available for course participants with detailed pointers to the literature. |
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Contact
Lectures
Lecture Notes Part 1 |
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Tutorials and Problems
In the tutorial, we will occasionally review topics from the lecture but mostly discuss problems and solutions to homework assignments. You are encouraged to pitch in by presenting a solution every once in a while.learn a few new things, expand on topics from class, and occasionally review exercises. Every week exercises will appear on this website. It is highly recommended for you to solve the most interesting and most important ones. Solutions to the most important exercises will appear on this website a week later. In order to encourage you to solve exercises, we will (1) periodically ask students to present solutions to an exercise in the tutorial and (2) base some of the exam questions on the exercises.Every week each student is required to solve homework assignments and hand them in. The problem sheets will be uploaded on Tuesdays and solutions should be turned in before the lecture on the following Tuesday. You will receive points for your solutions based on whether your solutions are correct and well-written. Course requirements are the following: (1) You must score at least 50% of the total points of the problems assigned in each half of the semester. There will be 6 problem sheets in the first half of the semester. A sheet will have problems worth roughly 20 pointsactively participate in the course. (2) You must pass an exam at the end of the semester which alone will determine your grade. Problem Sheets
The date for the exam will be available within the first 2 weeks of class. Problem SheetsSheet 12 (the last one!) (TeX) – updated |