The Snake Lemma and Indecomposable Chain Maps

Explore the intricacies of the snake lemma and indecomposable chain maps in this 45-minute lecture by Michael Robinson from the Applied Algebraic Topology Network. Delve into an alternative approach to understanding the snake lemma beyond the traditional diagram chase, focusing on the behavior of the connecting homomorphism and its induction from short exact sequences. Examine the special case of chain complexes of vector spaces, utilizing Escolar and Hiraoka's complete representation of chain maps. Discover the nine "easy" indecomposable chain maps and the crucial exceptional indecomposable that illuminates when the connecting homomorphism becomes nontrivial. Gain insights into the algorithmic study of homological algebra and simplified proofs through this characterization.