{"id":"hexagon/2610.00211","pdf":"https://hexagonmath.org/pdf/2610.00211v1","url":"https://hexagonmath.org/abs/2610.00211v1","tags":["msc:55M25","degree theory"],"score":0,"title":"Axiomatic degree theory on topological manifolds","domain":"math.AT","source":"hexagon","authors":["Stoyan Apostolov"],"reviews":0,"subject":"math.AT","summary":"In this note we study extension of standard Euclidean degree in nonlinear analysis to the setting of general oriented topological manifolds. The axiomatization of Euclidean degree is adapted to this setting. Existence and uniqueness are proven. The existence does not rely on smooth approximations as in the Euclidean case -- this is irrelevant for manifolds which do not admit a smooth structure and could be ambiguous for manifolds admitting many smooth structures. Rather, we rely on a cohomological approach using only topological information. When compared to the Euclidean case, we think this…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-12","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}