Problems in differential and algebraic topology
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Mapping spaces. Series 3. Series 4. Series 5. Half-exact functors. Series 6.
Algebraic Topology 1
Spaces related to Linear Algebra and their Homotopy Groups. Series 7. Homotopy classification of maps. Algebraic Topology as a separate filed of mathematics has not much more than years. Its aim is to study topological properties of spaces such that manifolds, polyhedra etc. It uses also analytic tools.
Introduction to Differential and Algebraic Topology
Fundamental notions of algebraic topology - homotopy and homology - were introduced by a great French mathematician Henri Poincare Poincare believed that those ideas will play a fundamental role in many mathematical fields, also far away from topology. His vision fulfilled - the methods of Algebraic Topology influenced very strongly development of mathematics in XX century.
To students interested in history of Algebraic Topology we recommend J.
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Adamsa Cambridge Univ. Here is another one.
Or Hyperbolic knots. All these sites are part of an exciting collection of knots and links available at "The KnotPlot Site". Very instructive are also the VRML knot models. Raytraced images: Sphere , Torus , projective plane: a Crosscap , a Steiner surface, a Boy surface , and a genus 3 orientable surface.
Download here a vrml viewer for Linux. David Eppstein's "Geometry Junkyard" : a collection of pointers, clippings, research blurbs, and other stuffs related to discrete, computational geometry, and topology. Paul Bourke's collection of raytraced surfaces. Here is for instance the animation of a transition from a Steiner surface into a Boy surface. Alexander Carney. Julian Chaidez. Ethan Dlugie. Kevin Donoghue. Christopher Eur. Benjamin Filippenko.
Scientific and Engineering Applications of Algebraic Topology
Benjamin Gammage. Andrew Hanlon. Jeff Hicks. Christopher Kuo. Hongyi Liu.
Calvin McPhail-Snyder. Kyle Miller. Mihai Munteanu. Eduardo Oregon Reyes.
Yingdi Qin. Eugene Rabinovich. Ritvik Ramkumar.
Alexander Sherman. Michael Smith. German Stefanich. Dun Tang. Luya Wang. Morgan Weiler. Ben Wormleighton. Xiaohan Yan.
Ziwen Zhao. Harrison Chen. Chris Gerig. Seiberg-Witten and Gromov invariants for self-dual harmonic 2-forms. Daniel Lowengrub. Applications of the Intersection Theory of Singular Varieties. Wolfgang Schmaltz. Vivek Shende, Richard E. Thunwa 'Nics' Theerakarn. Ryan George Thorngren. Franco Vargas Pallete. On Renormalized Volume. Patrick Wilson. Zhengyi Zhou. Kuan-Ying Fang. Alvin Kerber. Quasi-Fuchsian surface subgroups of infinite covolume Kleinian groups.
Christopher Policastro. Integral estimates for approximations by incompressible deformations. Qiao Zhou Elaine. Chang-Yeon Cho. Topological types of Algebraic stacks. Aaron Mazel-Gee. Goerss--Hopkins obstruction theory via model? Benjamin B. Christian Hilaire. Heather Lee. Eric C. Zachary Aaron Sylvan. Sebastian Hurtado.