For every there is a natural notion of topological degree for maps in which allows us to write that space as a disjoint union of classes,
For every pair , we show that the distance
equals the minimal -energy in . In the special case we deduce from the latter formula an explicit value: .
@article{CML_2018__10_1_125_0, author = {Itai Shafrir}, title = {On the distance between homotopy classes in $W^{1/p,p}({\protect \mathbb{S}}^1;{\protect \mathbb{S}}^1)$}, journal = {Confluentes Mathematici}, pages = {125--136}, publisher = {Institut Camille Jordan}, volume = {10}, number = {1}, year = {2018}, doi = {10.5802/cml.48}, mrnumber = {3869013}, language = {en}, url = {https://cml.centre-mersenne.org/articles/10.5802/cml.48/} }
TY - JOUR AU - Itai Shafrir TI - On the distance between homotopy classes in $W^{1/p,p}({\protect \mathbb{S}}^1;{\protect \mathbb{S}}^1)$ JO - Confluentes Mathematici PY - 2018 SP - 125 EP - 136 VL - 10 IS - 1 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.48/ DO - 10.5802/cml.48 LA - en ID - CML_2018__10_1_125_0 ER -
%0 Journal Article %A Itai Shafrir %T On the distance between homotopy classes in $W^{1/p,p}({\protect \mathbb{S}}^1;{\protect \mathbb{S}}^1)$ %J Confluentes Mathematici %D 2018 %P 125-136 %V 10 %N 1 %I Institut Camille Jordan %U https://cml.centre-mersenne.org/articles/10.5802/cml.48/ %R 10.5802/cml.48 %G en %F CML_2018__10_1_125_0
Itai Shafrir. On the distance between homotopy classes in $W^{1/p,p}({\protect \mathbb{S}}^1;{\protect \mathbb{S}}^1)$. Confluentes Mathematici, Volume 10 (2018) no. 1, pp. 125-136. doi : 10.5802/cml.48. https://cml.centre-mersenne.org/articles/10.5802/cml.48/
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