Analytic boundaries and constructible traces

Two lessons explain extensions of local systems across singular analytic boundaries and construct the supported trace class of a constructible complex. Thirteen exercises have complete solutions.

• Local systems across an analytic boundary · editable source
• Constructible traces and local Euler indices · editable source

The analytic-boundary theorem allows every commutative coefficient ring of finite global dimension, with nonzero coefficients specified in nonvanishing examples. The Euler-index and trace lesson uses a characteristic-zero field and retains its orientation, shift, boundedness and closed-support hypotheses. The geometric, perfect-duality and sheaf-operation prerequisites remain at their stated scopes.

The exact normalized maps are in these earlier lessons:

• Product evaluation with a cohomologically constructible factor
• Exceptional inverse image of internal Hom and exceptional composition

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Further sheaf proof readings include the linked constructibility and microlocal prerequisites with editable sources.