2022/12/14 by Friedman, Greg, Medina-Mardones, Anibal M., Sinha, Dev · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2212.07482
This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners. Special attention is given to the pull-back product of such smooth maps, which provides our geometric cochains with a partially defined product structure inducing the cup product in cohomology. A parallel treatment of homology is also given allowing for a geometric unification of the contravariant and covariant theories.