TY - JOUR

T1 - The order of a homotopy invariant in the stable case

AU - Podkorytov, S. S.

PY - 2011/10/21

Y1 - 2011/10/21

N2 - Let X, Y be cell complexes, let U be an Abelian group, and let f : [X, Y ]→U be a homotopy invariant. By definition, the invariant f has order at most r if the characteristic function of the rth Cartesian power of the graph of a continuous map a: X→ Y determines the value f([a]) Z-linearly. It is proved that, in the stable case (that is, when dim X > 2n-1, and Y is (n-1)-connected for some natural number n), for a finite cell complex X the order of the invariant f is equal to its degree with respect to the Curtis filtration of the group [X, Y ].

AB - Let X, Y be cell complexes, let U be an Abelian group, and let f : [X, Y ]→U be a homotopy invariant. By definition, the invariant f has order at most r if the characteristic function of the rth Cartesian power of the graph of a continuous map a: X→ Y determines the value f([a]) Z-linearly. It is proved that, in the stable case (that is, when dim X > 2n-1, and Y is (n-1)-connected for some natural number n), for a finite cell complex X the order of the invariant f is equal to its degree with respect to the Curtis filtration of the group [X, Y ].

KW - Curtis filtration

KW - Invariants of finite order

KW - Stable homotopy

UR - http://www.scopus.com/inward/record.url?scp=80054680637&partnerID=8YFLogxK

U2 - 10.1070/SM2011v202n08ABEH004183

DO - 10.1070/SM2011v202n08ABEH004183

M3 - Article

AN - SCOPUS:80054680637

VL - 202

SP - 1183

EP - 1206

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 8

ER -