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Luego de teoría de grupos, topología debe haber sido el primer tema "serio" que encontré en mi estudio de las matemáticas. Llegué a ella seguramente en los ochenta, y a la rama de topología general primero, y topología algebraica después. Estoy escribiendo sobre la primera en mi serie de posts.
Leo en la Wikipedia:
http://en.wikipedia.org/wiki/Topology
Topology (from the Greek τόπος, "place", and λόγος, "study") is a major area of mathematicsconcerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing, although the notion of stretching employed in mathematics is not quite the everyday notion: see below and the definition of homeomorphism for details of the mathematical notion. Topology emerged through the development of concepts fromgeometry and set theory, such as space, dimension, and transformation.
Ideas that are now classified as topological were expressed as early as 1736. Toward the end of the 19th century, a distinct discipline developed, which was referred to in Latin as the geometria situs("geometry of place") or analysis situs (Greek-Latin for "picking apart of place"). This later acquired the modern name of topology. By the middle of the 20th century, topology had become an important area of study within mathematics.
Vengo hoy esta primera entrega de enlaces:
Fürstenberg's proof of the infinitude of primes http://en.wikipedia.org/wiki/F%C3%BCrstenberg%27s_proof_of_the_infinitude_of_primes On Furstenberg"s Proof of the Infinitude of Primes http://www.idmercer.com/monthly355-356-mercer.pdf
The Birkhoff-Kakutani theorem http://terrytao.wordpress.com/2011/05/17/the-birkhoff-kakutani-theorem/
Physics - Weyl electrons kiss http://physics.aps.org/articles/v4/36 Topology, the mathematical description of the robustness of form, appears throughout physics, and provides strong constraints on many physical systems.
Milnor wins 2011 Abel Prize « Gowers's Weblog http://gowers.wordpress.com/2011/03/23/milnor-wins-2011-abel-prize/
YouTube - Cutting a Bagel http://www.youtube.com/watch?v=hYXnZ8-ux80
Mathematically Correct Breakfast -- Mobius Sliced Linked Bagel http://georgehart.com/bagel/bagel.html
Manifolds « The Unapologetic Mathematician http://unapologetic.wordpress.com/2011/02/22/manifolds/
Actualización de Entanglement, juego de cuerdas y nudos | Gaussianos http://gaussianos.com/actualizacion-de-entanglement-juego-de-cuerdas-y-nudos/
Nathaniel Johnston » The Maximum Score in the Game "Entanglement" is 9080 http://www.nathanieljohnston.com/2011/01/the-maximum-score-in-the-game-entanglement-is-9080/
El Topo Lógico: El Omegón y todo eso... (Parte 18) http://eltopologico.blogspot.com/2011/01/el-omegon-y-todo-eso-parte-18.html
Los topólogos predicen una nueva forma de la materia http://www.cienciakanija.com/2011/01/03/los-topologos-predicen-una-nueva-forma-de-la-materia
Doodling in Math Class http://golem.ph.utexas.edu/category/2010/12/doodling_in_math_class.html
Topology and Electromagnetism http://www.emph.com.ua/18/pdf/barrett.pdf
I Hate Math! (Not After This, You Won't) : Krulwich Wonders… : NPR http://www.npr.org/blogs/krulwich/2010/12/16/132050207/this-is-for-the-i-hate-math-crowd-not-after-this-you-won-t?ps=cprs
Physics of a Parallel Universe "Exerting a Ghostly Grip on Our Universe" http://www.dailygalaxy.com/my_weblog/2010/12/news-flash-new-form-of-matter-exerting-a-ghostly-grip-on-our-universe.html
Hilorama de E8 « Juegos topológicos http://topologia.wordpress.com/2010/10/10/e8-con-hilo-tensado/
A Concise Course in Algebraic Topology http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf
Mike on Topological Quantum Computing, at Georgia http://sbseminar.wordpress.com/2009/05/18/mike-on-topological-quantum-computing-at-georgia/
Icosien | GEEKY juegos http://geekyjuegos.com.ar/2010/06/icosien/
Motive-ating the Weil Conjecture Proof http://sbseminar.wordpress.com/2010/06/10/motive-ating-the-weil-conjecture-proof/ Algebraic topology, cohomology theories, and my idol, Grothendieck "Leverage the level of abstraction" with steroids ;-) Inside Grothendieck mind: http://www.jmilne.org/math/xnotes/mot.html
Mathematical Problem Solved After More Than 50 Years: Chern Numbers Of Algebraic Varieties http://www.sciencedaily.com/releases/2009/06/090610124858.htm
Poincaré Project http://jtauber.com/poincare_project/ Working through the mathematics required to understand the Poincaré Conjecture and the possible solution recently proposed.
The Poincaré Conjecture http://www.claymath.org/poincare/
on Topology http://ontopo.wordpress.com/
What is computational topology ? http://geomblog.blogspot.com/2009/11/what-is-computational-topology.html
Nonstandard analogues of energy and density increment arguments http://terrytao.wordpress.com/2009/11/16/nonstandard-analogues-of-energy-and-density-increment-arguments/
Convexity Using Metric Balls « on Topology http://ontopo.wordpress.com/2009/03/23/convexity-using-metric-balls/
The Topology of Higher-Dimensional Real Spaces « The Unapologetic Mathematician http://unapologetic.wordpress.com/2009/09/15/the-topology-of-higher-dimensional-real-spaces/
Solution of the Poincaré conjecture http://en.wikipedia.org/wiki/Hamilton%E2%80%93Perelman_solution_of_the_Poincar%C3%A9_conjecture
Open problems in algebraic topology http://claude.math.wesleyan.edu/~mhovey/problems/index.html
Algebraic Topology and Distributed Computing http://www.cs.brown.edu/~mph/topology.html Mis posts: Topología, Física y Solzhenitsyn http://ajlopez.zoomblog.com/archivo/2011/04/15/topologia-Fisica-y-Solzhenitsyn.html Motivado por este fragmento: http://www.maths.ed.ac.uk/~aar/surgery/first.pdf Vean que Solzhenitsyn estaba equivocado: la topología en física es hoy un tópico "caliente" en ciencia. Poincaré y la topología http://ajlopez.zoomblog.com/archivo/2007/02/01/poincare-y-la-topologia.html Felix Hausdorff por Laurence Young http://ajlopez.zoomblog.com/archivo/2011/05/05/felix-Hausdorff-por-Laurence-Young.html Abstracción y Definición en Matemáticas http://ajlopez.zoomblog.com/archivo/2011/05/02/abstraccion-y-Definicion-en-Matematica.html
Nos leemos!
Angel "Java" Lopez http://www.ajlopez.com http://twitter.com/ajlopez
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