Notes on Homology Theory - McGill School Of Computer Science
... In this work, we are mainly concerned with a special type of topological spaces, known as simplicial complexes. For an introduction to simplicial complexes, see Chapter ??. Here, we introduce some broader classes of topological spaces, namely the CW complexes and ∆-complexes. Simplicial complexes a ...
... In this work, we are mainly concerned with a special type of topological spaces, known as simplicial complexes. For an introduction to simplicial complexes, see Chapter ??. Here, we introduce some broader classes of topological spaces, namely the CW complexes and ∆-complexes. Simplicial complexes a ...
Modules Over Principal Ideal Domains
... Proposition 8. An abelian group G is finite if and only if it is a finitely generated torsion Z-module. Proof. Begin by noting that G is referred to in this proof both as a group and a module. But looking back at example 1, it should be clear that this is not a mistake, but a realization that the sc ...
... Proposition 8. An abelian group G is finite if and only if it is a finitely generated torsion Z-module. Proof. Begin by noting that G is referred to in this proof both as a group and a module. But looking back at example 1, it should be clear that this is not a mistake, but a realization that the sc ...
Quasi isometries of hyperbolic space are almost isometries
... extension to the sphere at infinity. A quasi-conformal map is differentiable a.e., and is therefore closely approximated by a linear map near a.e. point at infinity. At a.e. point the derivative is non-singular because quasi-conformal maps are absolutely continuous. The behaviour at infinity determi ...
... extension to the sphere at infinity. A quasi-conformal map is differentiable a.e., and is therefore closely approximated by a linear map near a.e. point at infinity. At a.e. point the derivative is non-singular because quasi-conformal maps are absolutely continuous. The behaviour at infinity determi ...
