# Surgery obstruction map I (Ex)

From Manifold Atlas

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## Latest revision as of 21:49, 29 May 2012

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].

## [edit] References

- [Ranicki2002] A. Ranicki,
*Algebraic and geometric surgery*, The Clarendon Press Oxford University Press, Oxford, 2002. MR2061749 (2005e:57075) Zbl 1003.57001