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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1998 • Question 16

Question

Math 6510 • Differentiable Manifolds Fall 1998 • Question 16

Prove that \(\mathbb {C}P^2\) cannot be decomposed as a union \(M_1\cup M_2\) where \(M_1\) and \(M_2\) are homeomorphic compact submanifolds with boundary and \(M_1\cap M_2\) is the common boundary of \(M_1\) and \(M_2\).

Raw LaTeX

Prove that \(\mathbb{C}P^2\) cannot be decomposed as a union \(M_1\cup M_2\) where
\(M_1\) and \(M_2\) are homeomorphic compact submanifolds with boundary and
\(M_1\cap M_2\) is the common boundary of \(M_1\) and \(M_2\).

Topic Tags

Smooth Manifolds and Embedded Submanifolds