Timeline for Topologists loops versus algebraists loops
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| Feb 27, 2010 at 3:00 | comment | added | S. Carnahan♦ | IIRC, Gr is homotopy equivalent to based polynomial loops. Laurent loops are analogous to unbased loops, and G[[t]] is homotopy equivalent to paths on G (and to G itself). | |
| Feb 26, 2010 at 13:23 | comment | added | GS | I have no idea about the general situation, but what you write is surely relevant: loops on G is homotopy equivalent to the affine Grassmannian of the complexification of G. There is a natural map from polynomial loops to the affine Grassmannian, and it induces an isomorphism on homology. So by standard graduate topology it's a homotopy equivalence. | |
| Feb 26, 2010 at 11:30 | history | answered | Andrew Stacey | CC BY-SA 2.5 |