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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1997 • Question 2

Question

Math 6510 • Differentiable Manifolds Fall 1997 • Question 2

Using homology prove Brouwer’s fixed-point theorem: If \(f:I^n\to I^n\) is a continuous map then there exists \(x\in I^n\) such that \(f(x)=x\). (Here and below \(I\) denotes the closed unit interval.)

Raw LaTeX

Using homology prove Brouwer's fixed-point theorem: If
\(f:I^n\to I^n\) is a continuous map then there exists \(x\in I^n\) such that \(f(x)=x\).
(Here and below \(I\) denotes the closed unit interval.)

Topic Tags

Cellular Homology Fixed Point Theorems and Borsuk-Ulam Homology with Coefficients Relative Homology and Long Exact Sequences