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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1999 • Question 13

Question

Math 6510 • Differentiable Manifolds Fall 1999 • Question 13

Find the Euler characteristic \(\chi (\mathbb {R}P^3\#(S^1\times S^2))\) of the connected sum.

In #14 and #15 by \(\Sigma _g\) we denote a closed oriented surface of genus \(g\).

Raw LaTeX

Find the Euler characteristic \(\chi(\mathbb{R}P^3\#(S^1\times S^2))\) of the
connected sum.

\textbf{In \#14 and \#15 by \(\Sigma_g\) we denote a closed oriented surface of genus
\(g\).}

Topic Tags

Euler Characteristic and Lefschetz Fixed Point Theorem Orientability and Volume Forms Smooth Manifolds and Embedded Submanifolds Surface Topology and Surface Groups