Topology/Exact Sequences

Topology Exact Sequences Homology Groups An exact sequence is a tool used in Algebraic Topology used to extract information from a sequence of chain groups. Definition Given a sequence of groups and homomorphisms is an exact sequence if for all , the sequence can be infinite. Given an exact sequence of chain groups, with this indexing we have a chain complex. Short Exact Sequence Given the special case where we have 3 groups with the following homomorphisms where is a one-one homomorphism and is an onto homomorphism, we have a short exact sequence. Short exact sequences have the property . Exercises (under construction) Topology Exact Sequences Homology Groups