What is "homologous map"? I'm reading a paper of Hillas about stability of game, and I found that the author uses a term "homologous" between continuous maps. I've never heard about such term before, and I can't find the definition in wikipedia. It seems that "homologous" is coarser than "homotopic", in the sense that if two continuous maps are homotopic then they are homologous. Also, the map is not homologous to a constant map if its graph has holes in it. It seems that this means the graph of the map is not null-homotopic. I can only find a definition of "homologous" between two paths, not two maps. Could you give a formal definition of the term "homologous"? Thanks in advance. Edit : Here is a link to the paper.

As far as I can tell, this is just an error on the part of the author (though it is possible that this terminology is standard in game theory; I haven't investigated thoroughly). When they refer to a map being "homologous to a trivial map", what they actually mean is just that the induced map on homology is zero (compare to the definition at < for instance, though that one uses cohomology instead of homology).