Timeline for Applications of topological chiral homology and factorization algebras (aka higher Hochschild cohomology)
Current License: CC BY-SA 3.0
4 events
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| Mar 10, 2014 at 22:38 | comment | added | Hiro Lee Tanaka | So I think the limitation isn't in the versatility of the invariants, but in the computability. Lifting Donaldson invariants to the spectrum level (Manolescu) or Casson invariants to a Floer cochain complex (Atiyah-Floer conjecture) are good examples. | |
| Mar 10, 2014 at 22:37 | comment | added | Hiro Lee Tanaka | While that might seem like a limitation, objects of a category are usually better invariants than numbers. For instance, if the target category is chain complexes, you get a number of invariants: Euler characteristic and (more generally) Betti numbers or cohomology groups of the chain complex. If your target is spaces, all of a space's topological invariants become an invariant... | |
| Mar 16, 2013 at 17:45 | comment | added | Peter May | Jacob himself is very forthright about the limitations of his Theorem 4.1.24 in his illuminating Remark 4.1.27, which starts out "Theorem 4.1.24 is usually not very satisfying, because it describes a functor ... whose values on closed framed n-manifolds are objects of an (\infty,1) category S, rather than concrete invariants like numbers". | |
| Mar 16, 2013 at 14:25 | history | answered | Dmitri Pavlov | CC BY-SA 3.0 |