Timeline for Lipschitz homotopy groups
Current License: CC BY-SA 4.0
8 events
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| Jan 25, 2019 at 23:23 | history | edited | Piotr Hajlasz | CC BY-SA 4.0 |
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| Mar 14, 2018 at 23:07 | comment | added | YCor | Actually I remember discussing this notion with Wenger (and others), and this was at the time of the previous article arxiv.org/abs/1004.2907 (in the IHP semester in January-March 2011). Basically it became transparent that his result was related to the fact that the asymptotic cone of the group in consideration has a nontrivial Lipschitz $\pi_1$. | |
| Mar 14, 2018 at 22:45 | comment | added | Piotr Hajlasz | The paper Lipschitz homotopy groups of the Heisenberg groups by Wenger and Young was written after ours, but published before ours. In fact, in the paper they answered some of the questions from our paper. | |
| Mar 14, 2018 at 22:35 | comment | added | YCor | Why do you say you haven't seen anything? In your paper you're quoting papers involving "lipschitz homotopy groups" (by Wenger-Young). | |
| Mar 14, 2018 at 20:32 | comment | added | mme | Ah, I see. Thank you for the point of clarification! | |
| Mar 14, 2018 at 20:04 | comment | added | Piotr Hajlasz | @Mike Miller In the case of smooth manifolds there is no difference between classical and Lipschitz homotopy groups. The difference is when we work with metric spaces. For example in the case of the Heisenberg groups the classical homotopy groups are trivial, because the space is homeomorphic to the Euclidean space, but some of the Lipschitz homotopy groups are not trivial. | |
| Mar 14, 2018 at 19:48 | comment | added | mme | The existence of smooth approximation (and relative smooth approximation) results, particularly those defined by convolution, lead me to expect that these agree with the standard homotopy groups. Intuitively they "fit between" smooth and continuous homotopy, which coincide. | |
| Mar 14, 2018 at 18:38 | history | asked | Piotr Hajlasz | CC BY-SA 3.0 |