On the distance between homotopy classes of maps between spheres

Shay Levi; Itai Shafrir

doi:10.1007/s11784-014-0156-5

On the distance between homotopy classes of maps between spheres

Shay Levi, Itai Shafrir

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

Certain Sobolev spaces of maps between manifolds can be written as a disjoint union of homotopy classes. Rubinstein and Shafrir [Israel J. Math. 160 (2007), 41–59] computed the distance between homotopy classes in the spaces W^1,p(S¹, S¹) for different values of p, and in the space W^1,2(Ω, S¹) for certain multiply connected two-dimensional domains Ω. We generalize some of these results to higher dimensions. Somewhat surprisingly we find that in W^1,p(S², S²), with p > 2, the distance between any two distinct homotopy classes equals a universal positive constant c(p). A similar result holds in W^1,p(Sⁿ, Sⁿ) for any n ≥ 2 and p > n.

Original language	English
Pages (from-to)	501-518
Number of pages	18
Journal	Journal of Fixed Point Theory and Applications
Volume	15
Issue number	2
DOIs	https://doi.org/10.1007/s11784-014-0156-5
State	Published - Jun 2014

Keywords

46E35
58D15

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Geometry and Topology
Applied Mathematics

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10.1007/s11784-014-0156-5

Cite this

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title = "On the distance between homotopy classes of maps between spheres",

abstract = "Certain Sobolev spaces of maps between manifolds can be written as a disjoint union of homotopy classes. Rubinstein and Shafrir [Israel J. Math. 160 (2007), 41–59] computed the distance between homotopy classes in the spaces W1,p(S1, S1) for different values of p, and in the space W1,2(Ω, S1) for certain multiply connected two-dimensional domains Ω. We generalize some of these results to higher dimensions. Somewhat surprisingly we find that in W1,p(S2, S2), with p > 2, the distance between any two distinct homotopy classes equals a universal positive constant c(p). A similar result holds in W1,p(Sn, Sn) for any n ≥ 2 and p > n.",

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T1 - On the distance between homotopy classes of maps between spheres

AU - Levi, Shay

AU - Shafrir, Itai

PY - 2014/6

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N2 - Certain Sobolev spaces of maps between manifolds can be written as a disjoint union of homotopy classes. Rubinstein and Shafrir [Israel J. Math. 160 (2007), 41–59] computed the distance between homotopy classes in the spaces W1,p(S1, S1) for different values of p, and in the space W1,2(Ω, S1) for certain multiply connected two-dimensional domains Ω. We generalize some of these results to higher dimensions. Somewhat surprisingly we find that in W1,p(S2, S2), with p > 2, the distance between any two distinct homotopy classes equals a universal positive constant c(p). A similar result holds in W1,p(Sn, Sn) for any n ≥ 2 and p > n.

AB - Certain Sobolev spaces of maps between manifolds can be written as a disjoint union of homotopy classes. Rubinstein and Shafrir [Israel J. Math. 160 (2007), 41–59] computed the distance between homotopy classes in the spaces W1,p(S1, S1) for different values of p, and in the space W1,2(Ω, S1) for certain multiply connected two-dimensional domains Ω. We generalize some of these results to higher dimensions. Somewhat surprisingly we find that in W1,p(S2, S2), with p > 2, the distance between any two distinct homotopy classes equals a universal positive constant c(p). A similar result holds in W1,p(Sn, Sn) for any n ≥ 2 and p > n.

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DO - 10.1007/s11784-014-0156-5

M3 - مقالة

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VL - 15

SP - 501

EP - 518

JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

IS - 2

ER -

On the distance between homotopy classes of maps between spheres

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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