What is...the Poincaré conjecture? скачать в хорошем качестве

What is...the Poincaré conjecture?

Goal. Explaining basic concepts of geometric topology in an intuitive way. This time. What is...the Poincaré conjecture? Or: Spheres will be spheres. Disclaimer. Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references. Disclaimer. Geometric topology is usually the study of manifolds. This can mean manifold things ;-) So to be precise, this video series is mostly about knots, surfaces, three and four manifolds. Warning. There is a historical error in the video and on the slides: As pointed out in the comments, the topological n=4 case is due to Freedman not Smale. Slides. http://www.dtubbenhauer.com/youtube.html Website with exercises. http://www.dtubbenhauer.com/lecture-g... Thumbnail. Picture from    • What is...exotic four space?   Geometric topology. https://en.wikipedia.org/wiki/Geometr... https://en.wikipedia.org/wiki/List_of... https://en.wikipedia.org/wiki/Manifold https://en.wikipedia.org/wiki/Knot_(m...) https://en.wikipedia.org/wiki/Surface...) https://en.wikipedia.org/wiki/3-manifold Concepts in geometric topology. https://en.wikipedia.org/wiki/Knot_in... https://en.wikipedia.org/wiki/Braid_g... https://en.wikipedia.org/wiki/Euler_c... https://en.wikipedia.org/wiki/Mapping... https://en.wikipedia.org/wiki/Exotic_... https://en.wikipedia.org/wiki/Poincar... https://en.wikipedia.org/wiki/Thursto... https://en.wikipedia.org/wiki/Cobordism https://en.wikipedia.org/wiki/Unknott... Applications of geometric topology. https://physics.stackexchange.com/que... https://mathoverflow.net/questions/48... https://math.mit.edu/research/highsch... The wild world of four manifolds. https://en.wikipedia.org/wiki/4-manifold https://en.wikipedia.org/wiki/Categor... https://arxiv.org/abs/math/0610700 https://web.stanford.edu/~cm5/4D.pdf https://bookstore.ams.org/gsm-20 https://global.oup.com/academic/produ... https://en.wikipedia.org/wiki/Four-di... History of topology. https://www.elsevier.com/books/histor... https://en.wikipedia.org/wiki/Analysi...) https://gallica.bnf.fr/ark:/12148/bpt... https://www.maths.ed.ac.uk/~v1ranick/... Poincare conjecture and h-cobordism. https://en.wikipedia.org/wiki/Poincar... https://en.wikipedia.org/wiki/General... https://www.jstor.org/stable/1970239?... https://en.wikipedia.org/wiki/H-cobor... https://mathworld.wolfram.com/h-Cobor... Pictures used. Picture from https://gallica.bnf.fr/ark:/12148/bpt... https://encrypted-tbn0.gstatic.com/im... https://encrypted-tbn0.gstatic.com/im... https://intuitivescienceblog.files.wo... Picture from https://www.jstor.org/stable/1970239?... https://en.wikipedia.org/wiki/Cobordi... Picture from    • What is...exotic four space?   Some books I am using (I sometimes steal some pictures from there). https://www.math.cuhk.edu.hk/course_b... https://arxiv.org/abs/1610.02592?cont... https://www.degruyter.com/document/do... https://bookstore.ams.org/fourman https://www.degruyter.com/document/do... https://bookstore.ams.org/surv-55 https://bookstore.ams.org/gsm-20 KnotAtlas. http://katlas.math.toronto.edu/wiki/T... SnapPy. https://snappy.math.uic.edu/ Mathematica. http://katlas.org/wiki/The_Mathematic... https://demonstrations.wolfram.com/Ch... SageMath. https://doc.sagemath.org/html/en/refe... #geometrictopology #topology #mathematics