Reducible Poincaré Complexes (Ex)
From Manifold Atlas
Exercise 0.1. Let be a finite Poinaré complex of formal dimension with Spivak Normal Fibration . A theorem of Wall, [Wall1967a, Theorem 2.4], states that may be written
where has dimension less than . Show that for some , the top cell of splits off, i.e. , if and only if , the Spivak normal fibration of , is trivial.
[edit] References
- [Wall1967a] C. T. C. Wall, Poincaré complexes. I, Ann. of Math. (2) 86 (1967), 213–245. MR0217791 (36 #880)