Topological Invariants of Stratified Spaces

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Poincaré duality is a central theme, illustrating the symmetry in the homology of manifolds, particularly in triangulated manifolds. The text explores how dual blocks in barycentric subdivisions relate to cell complexes, leading to the computation of manifold homology. It further delves into the classification of manifolds through surgery and the significance of the signature as a bordism invariant. Additionally, the book addresses the challenges of applying these concepts to singular spaces, where traditional duality does not hold, and investigates the establishment of invariants in this context.