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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2014 • Question 12

Question

Math 6510 • Differentiable Manifolds Spring 2014 • Question 12

Let \(M\) be a connected compact 3-manifold (without boundary) and assume that \(H_1(M)=\mathbb {Z}/3\mathbb {Z}\). Find \(H_2(M)\). Carefully justify the answer, and state all theorems you are using.

Raw LaTeX

Let \(M\) be a connected compact 3-manifold (without boundary) and assume
that \(H_1(M)=\Z/3\Z\). Find \(H_2(M)\). Carefully justify the answer, and state all
theorems you are using.

Topic Tags

Fundamental Groups Homotopy and Degree on Manifolds Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds