# Splitting invariants (Ex)

From Manifold Atlas

Revision as of 14:22, 23 March 2012 by Marek Kaluba (Talk | contribs)

Prove that two maps are homotopic iff their splitting invariants agree for .

Use the exact sequence

and the fact that the surgery obstruction map

splits the above sequence for . Additionally and the isomorphism is given by the surgery obstruction map.