{"id":2317,"date":"2024-01-18T15:57:29","date_gmt":"2024-01-18T20:57:29","guid":{"rendered":"https:\/\/brickisland.net\/DDGSpring2024\/?p=2317"},"modified":"2024-01-18T15:57:29","modified_gmt":"2024-01-18T20:57:29","slug":"lecture-2-combinatorial-surfaces","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2024\/2024\/01\/18\/lecture-2-combinatorial-surfaces\/","title":{"rendered":"Lecture 2\u2014Combinatorial Surfaces"},"content":{"rendered":"<p><a href=\"http:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2024\/01\/DDG_458_SP24_Lecture02_CombinatorialSurfaces.pdf\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2318\" src=\"http:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2024\/01\/CombinatorialSurfaces.jpg\" alt=\"\" width=\"1920\" height=\"1080\" srcset=\"https:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2024\/01\/CombinatorialSurfaces.jpg 1920w, https:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2024\/01\/CombinatorialSurfaces-300x169.jpg 300w, https:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2024\/01\/CombinatorialSurfaces-1024x576.jpg 1024w, https:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2024\/01\/CombinatorialSurfaces-768x432.jpg 768w, https:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2024\/01\/CombinatorialSurfaces-1536x864.jpg 1536w, https:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2024\/01\/CombinatorialSurfaces-1200x675.jpg 1200w\" sizes=\"(max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><br \/>Slides (PDF)<\/a><\/p>\n<p>This lecture gives one precise definition to the notion of a &#8220;mesh,&#8221; namely a <em>simplicial complex<\/em>.\u00a0 If we consider only the connectivity of a simplicial complex, rather than any locations for its vertices in space, we get an <em>abstract simplicial complex<\/em>.\u00a0 From the perspective of differential geometry, an <em>abstract simplicial complex<\/em> plays the role of a so-called topological space, telling us how the domain is &#8220;connected up,&#8221; without saying anything specific about its geometry.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Slides (PDF) This lecture gives one precise definition to the notion of a &#8220;mesh,&#8221; namely a simplicial complex.\u00a0 If we consider only the connectivity of a simplicial complex, rather than any locations for its vertices in space, we get an abstract simplicial complex.\u00a0 From the perspective of differential geometry, an abstract simplicial complex plays the &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2024\/2024\/01\/18\/lecture-2-combinatorial-surfaces\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Lecture 2\u2014Combinatorial Surfaces&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":"","_links_to":"","_links_to_target":""},"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/2317"}],"collection":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/comments?post=2317"}],"version-history":[{"count":1,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/2317\/revisions"}],"predecessor-version":[{"id":2320,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/2317\/revisions\/2320"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/media?parent=2317"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/categories?post=2317"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/tags?post=2317"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}