I'm reading about obstruction theory. It's said that difference cochain $\delta (f_n,g_n)$ has properties:

$\delta(f_n,g_n)=0$ iff $f_n\simeq g_n (rel X_{n-1})$.




I'm looking for book or lectures where these properties are proved. Also, detailed answers would be really helpful.

Thanks in advance.

  • $\begingroup$ Munkres, Elements of algebraic topology. $\endgroup$ – Peter Franek Jan 13 '17 at 10:18

In Whitehead's (1978) textbook "Elements of homotopy theory" you can find a chapter 5 "Obstruction Theory" (pp. 228 - 235).

For most of your properties you will find a proof in "Obstruction Theory: On Homotopy Classification of Maps" by H. J. Baues (1977), e.g. on pp. 261 (4.2.9 "Obstruction theorem") you will find a proof for property 1 and 4.

Also Spanier's (1966) "Algebraic topology" (pp. 269 - 276, 429 - 432) will give some hints.


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