TY - JOUR

T1 - Mappings of the sphere to a simply connected space

AU - Podkorytov, S. S.

PY - 2007/1/1

Y1 - 2007/1/1

N2 - Fix an m ε N, m ≥ 2. Let Y be a simply connected pointed CW-complex, and let B be a finite set of continuous mappings a: Sm → Y respecting the distinguished points. Let Γ(a) ⊂ Sm × Y be the graph of a, and we denote by [a] πm(Y) the homotopy class of a. Then for some r ε N depending on m only, there exist a finite set E ⊂ Sm × Y and a mapping k: E(r) = {F ⊂ E: |F| ≤ r} → πm(Y) such that for each a ε B we have [a] = ∑FεE(r):F⊂Γ(a). Bibliography: 5 titles.

AB - Fix an m ε N, m ≥ 2. Let Y be a simply connected pointed CW-complex, and let B be a finite set of continuous mappings a: Sm → Y respecting the distinguished points. Let Γ(a) ⊂ Sm × Y be the graph of a, and we denote by [a] πm(Y) the homotopy class of a. Then for some r ε N depending on m only, there exist a finite set E ⊂ Sm × Y and a mapping k: E(r) = {F ⊂ E: |F| ≤ r} → πm(Y) such that for each a ε B we have [a] = ∑FεE(r):F⊂Γ(a). Bibliography: 5 titles.

UR - http://www.scopus.com/inward/record.url?scp=33845799840&partnerID=8YFLogxK

U2 - 10.1007/s10958-007-0441-6

DO - 10.1007/s10958-007-0441-6

M3 - Article

AN - SCOPUS:33845799840

VL - 140

SP - 589

EP - 610

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -