{"id":2321,"date":"2024-01-18T16:03:23","date_gmt":"2024-01-18T21:03:23","guid":{"rendered":"https:\/\/brickisland.net\/DDGSpring2024\/?p=2321"},"modified":"2024-01-18T16:03:23","modified_gmt":"2024-01-18T21:03:23","slug":"lecture-2b-introduction-to-manifolds","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2024\/2024\/01\/18\/lecture-2b-introduction-to-manifolds\/","title":{"rendered":"Lecture 2B\u2014Introduction to Manifolds"},"content":{"rendered":"

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Slides (PDF)<\/br><\/a><\/p>\n

In this lecture we connect what we learned on the discrete side last time, about combinatorial surfaces and the simplicial complex, to manifolds, which are a central object in differential geometry. Manifolds are, very<\/em> roughly speaking, a “particularly nice kind of (topological) space,” where concepts like “the neighborhood around a point” are always well-defined, and always look the same. By imposing an additional regularity condition on simplicial complexes, we likewise get a simplicial manifold<\/em>, which more informally can be thought of as a “particularly nice kind of mesh.” In terms of practical algorithms, it’s often useful to assume manifold input, because it allows you to write code without worrying about tricky special cases.<\/p>\n","protected":false},"excerpt":{"rendered":"

Slides (PDF) In this lecture we connect what we learned on the discrete side last time, about combinatorial surfaces and the simplicial complex, to manifolds, which are a central object in differential geometry. Manifolds are, very roughly speaking, a “particularly nice kind of (topological) space,” where concepts like “the neighborhood around a point” are always … Continue reading “Lecture 2B\u2014Introduction to Manifolds”<\/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\/2321"}],"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=2321"}],"version-history":[{"count":1,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/2321\/revisions"}],"predecessor-version":[{"id":2324,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/2321\/revisions\/2324"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/media?parent=2321"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/categories?post=2321"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/tags?post=2321"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}