In mathematics , the puppet sequence is a construction of the homotopy theory .
It was introduced by Dieteruppe in 1958 and is also known as the doll sequence .
definition
Let it be a continuous mapping . Let it be the mapping cone of , then is
a cofiber and
is the attachment of . By iterating, what is known as the doll sequence is obtained
application
For a continuous mapping and for every space , the homotopy classes of continuous mapping form an exact sequence
Individual evidence
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↑ Dieter Doll: Homotopiemengen and their induced illustrations , Part I, Mathematical Journal, Vol 69, 1958, pp 299-344
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↑ James C. Becker, Daniel Gottlieb: A history of duality in algebraic topology , pdf
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↑ Tammo tom Dieck: Topology , 2. completely revised. and exp. Edition, de Gruyter (2000), pp. 202ff, ISBN 3-11-016236-9