Surgery obstruction map I (Ex)

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Latest revision as of 21:49, 29 May 2012

Show that the surgery obstruction map

\displaystyle  \theta \colon \mathcal{N} (X) \rightarrow L_{n} (\Zz [\pi_1 (X)])

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 n = 4k, find a formula for \theta in terms of the \mathcal{L}-class. See Exercise 13.3 in [Ranicki2002].

[edit] References

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