Surgery obstruction map I (Ex)
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Show that the surgery obstruction map
is not in general a homomorphism of abelian groups, when the normal invariants are viewed as an abelian group with the group structure coming from the Whitney sum of vector bundles.
Hint: in the simply connected case and , find a formula for in terms of the -class. See Exercise 13.3 in [Ranicki2002].
References
- [Ranicki2002] A. Ranicki, Algebraic and geometric surgery, The Clarendon Press Oxford University Press, Oxford, 2002. MR2061749 (2005e:57075) Zbl 1003.57001