2016/08/01 by Jan Steinebrunner, Steinebrunner, Jan
Mathematics · #55-01 #55N10 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:55-01 #msc:55N10
paper · pdf · doi:10.48550/arxiv.1608.00483
23 pages, 3 figures
arxiv created 2016/08/01 · arxiv updated 2016/08/02
This article shows several new methods for proofs on Kan complexes while using them to give a compact introduction to the homotopy groups of these complexes. Then more advanced objects are studied starting with homology and the Hurewicz homomorphism. Eilenberg-Mac Lane-spaces are constructed explicitly and can then be used to define spectral cohomology. In the end the equivalence to the usual simplicial cohomology is shown.