何为‘homologous map’？博弈稳定性论文相关技术问询

Hey there! I get why this term is confusing—it’s not as widely covered in introductory topology resources, and even Wikipedia doesn’t have a straightforward entry tailored to this context. Let me walk through what I’ve pieced together from your observations and standard topology principles:

• You’re spot-on about the relationship between homologous and homotopic: If two continuous maps are homotopic, they are definitely homologous, but homology is a broader equivalence relation than homotopy. That means there are pairs of maps that are homologous but not homotopic.
• The hole-related behavior you noticed is a core part of homology’s purpose. Homology is all about detecting "holes" in topological spaces (or in the images of maps, in this case). If a map’s image contains a hole, it can’t be homologous to a constant map—since a constant map’s image is just a single point, with no holes to track. This aligns with the fact that such a map isn’t null-homotopic either: a null-homotopic map can be continuously shrunk down to a single point, which is impossible if the image has a hole that prevents that contraction.

内容的提问来源于stack exchange，提问作者Seewoo Lee