Algebraic Topology: A First CourseWorld Publishing Corporation, 1995 - 430 pages Introduces 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 analytic Aut(Y/X b₁ base point boundary Chapter circle closed 1-chain closed 1-form closed paths cocycle cohomology compact complement complex connected components construct contained continuous mapping coordinate Corollary corresponding covering map define denoted determines diffeomorphic differential disjoint union disk element endpoints equivalence Exercise fact finite number follows formula free abelian group function f fundamental group G-covering group G H₁U H₁X homology group homomorphism homotopy integral isomorphism k-form Lemma lifting linear map locally constant locally constant functions locally path-connected loop Mayer-Vietoris meromorphic function morphism neighborhood nonzero open sets P₁ plane Problem Proof Proposition prove quotient rectangle Rham Riemann surface Show simply connected sphere subgroup subspace Suppose surjective T₁ takes theorem topological space topology triangulation trivial U₁ unique universal covering vector field vector space Verify w₁ winding number Y₁ zero α α