We study Lefschetz fixed point formulas for constructible sheaves with higherdimensional fixed point sets. Under fairly weak assumptions, we prove that the local contributions from them are expressed by some constructible functions associated to hyperbolic localizations. This gives an affirmative answer to a conjecture of Goresky- MacPherson  in particular for smooth fixed point components (see [9, page 9, (1.12) Open problems]). In the course of the proof, the new Lagrangian cycles introduced in our previous article  will be effectively used. Moreover, we show various examples for which local contributions can be explicitly determined by our method.
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