Techniques of Geometric Topology

a₁ Abelian action Algebraic topology arcs associated assume base basic basis boundary calculated called cell complex Chapter circle closed cochain cocycle cohomology commutator components connected consider contains continuous corresponding cover crossed cup product cycle defined Definition denote dimension disc disjoint doodle dual edge element equivalent example field Figure fixed formula fundamental geometric given gives H₁ homology homomorphism homotopy identified identity induces integer invariant isometry isomorphism knot Lemma lies lift loop manifold Massey products Math module moves Note obtained orientation pair path picture plane presentation projection Proof properties prove relations represented result satisfying sequence Show simplex space string subgroup Suppose surface takes Theorem theory transverse trivial unique universal cover vector vertices zero