Hey, Internet, I’m talking about math today so check me out, d00dz:
Homotopy Theory from Top to Spectra: “Everything I see becomes a category to me!”
5:30pm Brown Math Dept Providence, RI FREE!
The category Top has Topological spaces as Objects and continuous maps as Morphisms. We typically analyze Top via the better understood category of (abelian) Groups using canonical functors (Top — pi_n –> Groups) called homotopy groups. A “weak equivalence” in Top is defined as a map A -> B such that pi_n(A) -> pi_n(B) is an isomorphism for all n. By formally inverting these weak equivalences in Top, we obtain the “derived/homotopy category” hTop which contains all the data of Top “up to weakequivalence/homotopy“. This category is extremely useful for understanding a variety of “homotopically meaningful” constructions. For my purposes I will focus on the relationships between “homotopy functors” hTop -> hTop, functors hTop -> Groups (eg. homotopy groups and (co)homology theories) and how all of these are related through magical categories called “Spectra“. I hope to sketch the big picture (as I currently understand it) without too many details.
6 responses so far ↓
Hans // Apr 25, 2007 at 2:15 pm
nice hour and 15 minutes notice!
s. frank // Apr 25, 2007 at 3:26 pm
i coulda given 2 years notice. it’ll still just be me and a math crue of maybe 10 peeps….
samuel venuti // Apr 25, 2007 at 11:24 pm
ummm…. i feel so dumb,.
Hans // Apr 26, 2007 at 7:20 am
i wish this was our first podcast!
even though i’d understand none of it.
joey greco // Apr 26, 2007 at 8:48 am
sweet animated gif. FV needs more ani gifs.
s. frank // Apr 26, 2007 at 11:55 am
nah, sam, you could figure this all out if you were dumb enough to waste your whole life in school.
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