Constructible duality and infinite twists

Learn how the actual Verdier-duality maps reverse inverse and direct images, why a nonproper image needs a second constructibility input, and how an infinite locally constant twist can preserve the comparison when the untwisted object has finite boundary control. Eight exercises have complete solutions.

• Duality maps for constructible inverse and direct images · editable source
• Natural comparisons with infinite locally constant coefficients · editable proof selection

The lesson uses a commutative ring of finite global dimension, bounded complexes and the stated finite-dimensional analytic-manifold conventions. The nonproper twisted direct-image theorem uses b-analytic pairs, a subanalytic ambient graph and an untwisted zero extension with perfect stalks. The twist itself may be infinite and need not extend across the ambient boundary. Orientations, shifts and canonical evaluation order are retained.

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