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In this chapter we prove a Poincaré duality theorem on non-orientable manifolds, and we also construct shriek maps in that setting. Along the way we recast the definition of the Morse complex with DG-coefficients using the notion of orientation line.

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Shriek Maps and Poincaré Duality for Non-Orientable Manifolds

  • 章节

  • 发表日期：

    2025年

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  • Jean-François Barraud,
  • Mihai Damian,
  • Vincent Humilière,
  • Alexandru Oancea

摘要

In this chapter we prove a Poincaré duality theorem on non-orientable manifolds, and we also construct shriek maps in that setting. Along the way we recast the definition of the Morse complex with DG-coefficients using the notion of orientation line.