Abstract:Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F right-arrow upper E right-arrow upper B"> <mml:semantics> <mml:mrow> <mml:mi>F...Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F right-arrow upper E right-arrow upper B"> <mml:semantics> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo stretchy="false">→</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy="false">→</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">F \to E \to B</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a fibration such that <italic>F</italic>, <italic>E</italic>, and <italic>B</italic> are homotopy equivalent to finite complexes. Then the following fact is proved. <italic>E</italic> is a Poincaré duality space if and only if <italic>B</italic> and <italic>F</italic> are Poincaré duality spaces.Read More