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Algebraic Topology

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Homotopy theory, homological algebra, algebraic treatments of manifolds || part of #mathematics-on:matrix.org8 Servers

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@smtilson:matrix.orgSean Tilson I think SW duality is best understood from the perspective of spectra. The fact that there is a space level model is pretty crazy. But I think one sees relatively quickly that it can be a bit hard to define. But now I see why you are mentioning SW duality. things move so slow here I forgot about the earlier conversation. 17:49:02
@smtilson:matrix.orgSean TilsonBut I am biased.17:49:13
@smtilson:matrix.orgSean TilsonRedacted or Malformed Event17:49:22
@smtilson:matrix.orgSean Tilson The pair A\times A' inside B \times B has the property that if you pull it back along the diagonal B \to B \times B you get the empty set, because this models the intersection. 17:50:31
@smtilson:matrix.orgSean TilsonI think the only kind of universal property you will end up getting is what you would expect given that A' is the complement of A in B.17:51:01
@smtilson:matrix.orgSean Tilson
In reply to @joel135:matrix.org
Maybe this is related to my previous question. I didn't dive deep into SW duality.
* I think SW duality is best understood from the perspective of spectra. The fact that there is a space level model is pretty crazy. But I think one sees relatively quickly that it can be a bit hard to define. But now I see why you are mentioning SW duality. things move so slow here I forgot about the earlier conversation.
17:52:52
@smtilson:matrix.orgSean Tilson Joel Sjögren: do you have a particular interest in Alexander Cech duality? Or is there some geometry you want to do? Or are you learning for fun? I just ask because if you are learning for fun, a friend of mine is posting some videos on youtube that I think are quite good, but they come after a couple semesters of Algebraic topology. 18:02:23
@smtilson:matrix.orgSean TilsonAlso, I just found that Borcherds has been uploading lectures to youtube. I have liked what I have seen so far and he does have a course on Algebraic Topology.18:02:53
10 Jul 2021
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28 Jul 2021
@joel135:matrix.orgJoel Sjögren
In reply to @smtilson:matrix.org
Joel Sjögren: do you have a particular interest in Alexander Cech duality? Or is there some geometry you want to do? Or are you learning for fun? I just ask because if you are learning for fun, a friend of mine is posting some videos on youtube that I think are quite good, but they come after a couple semesters of Algebraic topology.
I am thinking about logical negation, which is related to duality or adjointness by the identity rules of Girard's proof nets. So I am interested in all dualities, you could say. But in particular I am looking at how to model space with string diagrams for n-categories and the operations you can apply to such models, some of which are involutions or approximately involutions, and I am sometimes trying to match these with known instances of duality in geometry/topology.
06:22:40
@joel135:matrix.orgJoel SjögrenIf you tell me what the videos are I'll bookmark them 🙂06:23:39
30 Jul 2021
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2 Aug 2021
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