Algebraic Topology: A First CourseIntroduces the important ideas of algebraic topology by emphasizing the relation of these ideas with other areas of mathematics. This title focuses on concrete problems in spaces with a few dimensions, introducing only as much algebraic machinery as necessary for the problems encountered. |
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1-cycle a₁ Algebraic analytic Aut(Y/X base point boundary Chapter circle closed 1-chain closed 1-form closed paths cohomology compact complement complex connected components constant path construct contained continuous mapping coordinate Corollary covering map define denoted determines diffeomorphic differential disk element endpoints equivalence exact Exercise fact follows formula free abelian group function f fundamental group G-covering group G H₁U H₁X homology group homomorphism homotopy identity map integral interval isomorphism Jordan curve theorem Lemma lifting locally constant locally constant function locally path-connected loop mapping f Mayer-Vietoris meromorphic neighborhood open set P₁ Problem Proof Proposition prove quotient rectangle restriction Rham Riemann surface semilocally simply connected sequence Show simply connected singularities sphere subgroup Suppose surjective t₁ takes theorem topology trivial U₁ unique universal covering vector field vector space winding number y₁ zero