Manifolds and Maps

  • Morris W. Hirsch
Part of the Graduate Texts in Mathematics book series (GTM, volume 33)


Differential topology is the study of differentiable manifolds and maps. A manifold is a topological space which locally looks like Cartesian n-space ℝ n ; it is built up of pieces of ℝn glued together by homeomorphisms. If these homeomorphisms are differentiable we obtain a differentiable manifold.


Open Subset Tangent Vector Tangent Bundle Local Representation Coordinate Change 


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  1. 1.
    For r = 0 this is sometimes called a locally flat C0 submanifold.Google Scholar
  2. 2.
    This is in accordance with the principle that in mathematics a red herring does not have to be either red or a herring.Google Scholar
  3. 3.
    This means that D n(p) = {x∈ℝn:∣x∣ < p}; the unit disk is Δn = D n(1).Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1976

Authors and Affiliations

  • Morris W. Hirsch
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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