Poincar ́e Duality for Complexes of Sheaves

Student: Kaddaj Philip nikolay

Educational Programme: Mathematics (Bachelor)

Final Grade: 9

Year of Graduation: 2024

Classical Poincar\'e duality gives an isomorphism between the homology and cohomology of a compact oriented manifold without boundary by capping with the fundamental class. Generalisations of this have been constructed in a functorial manner by Verdier and in a topological manner by Borel and Moore. We extend the results of Borel and Moore by defining relative sheaf homology for pairs with coefficients in a complex of sheaves of $R$-modules (for an arbitrary ring $R$) and deduce a proof of Poincar\'e duality.

Full text (added May 31, 2024)

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