Osaka Journal of Mathematics

Self-coincidence of fibre maps

Albrecht Dold and Daciberg Lima Gonçalves

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Abstract

We study coincidence points for maps $f_1,f_2\colon E \to B$ into manifolds such that $f_1$ is homotopic to $f_2$. We analyze the first and higher obstructions to deform $f_1$ away to $f_2$. The main results consist in solving this one problem for the (generalized) Hopf bundles, which are $G$-principal bundles $p_nG \colon E_n G \to B_n G$ (the $n$-th stage of Milnor's construction), with $G= S^1,S^3$. We also consider the question for general maps $f\colon E_n G \to B_n G$ with $G= S^1,S^3$.

Article information

Source
Osaka J. Math., Volume 42, Number 2 (2005), 291-307.

Dates
First available in Project Euclid: 21 July 2006

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1153494379

Mathematical Reviews number (MathSciNet)
MR2147735

Zentralblatt MATH identifier
1079.55006

Citation

Dold, Albrecht; Gonçalves, Daciberg Lima. Self-coincidence of fibre maps. Osaka J. Math. 42 (2005), no. 2, 291--307. https://projecteuclid.org/euclid.ojm/1153494379


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