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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2010 • Question 18

Question

Math 6510 • Differentiable Manifolds Spring 2010 • Question 18

Let \(M\) be a connected topological \(n\)-manifold. Define what it means for \(M\) to be orientable. Then state the Poincaré duality theorem (including a careful definition of the map that is claimed to be an isomorphism).

Raw LaTeX

Let \(M\) be a connected topological \(n\)-manifold. Define what it means for
\(M\) to be orientable. Then state the Poincar\'e duality theorem (including a
careful definition of the map that is claimed to be an isomorphism).

Topic Tags

Homotopy and Degree on Manifolds Orientability and Volume Forms Poincare Duality Smooth Manifolds and Embedded Submanifolds