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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1995 • Question 1

Question

Math 6510 • Differentiable Manifolds Fall 1995 • Question 1

Let \(S_1\) and \(S_2\) be two (2-dimensional) surfaces. Derive the relationship between the Euler characteristic of the connected sum \(S_1\#S_2\) and the Euler characteristics of \(S_1\) and \(S_2\).

Raw LaTeX

Let \(S_1\) and \(S_2\) be two (2-dimensional) surfaces. Derive the
relationship between the Euler characteristic of the connected sum \(S_1\#S_2\) and
the Euler characteristics of \(S_1\) and \(S_2\).

Topic Tags

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