{"id":"palomar/PALOMAR-2026-10-05-000001","url":"https://github.com/Arthur742Ramos/higher-cell-attachment-lean/tree/bcf788e349b4969f4d8379ee9cb4df7a28352af1","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-05-000001-v1.json","repo":"https://github.com/Arthur742Ramos/higher-cell-attachment-lean","tags":["math.AT","math.CT","msc:55Q05","msc:18B40","algebraic-topology","fundamental-group","homotopy-theory","cell-attachment"],"score":0,"title":"Fundamental Groups of Arbitrary Higher-Cell Attachments","trust":"high","domain":"math.AT","source":"palomar","authors":["Arthur Freitas Ramos","David Barros Hulak","Ruy Jose Guerra Barretto de Queiroz"],"reviews":0,"subject":"math.AT","summary":"Higher-cell attachment invariance for ordinary topological fundamental groups. For any path-connected topological space X, any basepoint, an index type in an independent universe, independently varying cell dimensions at least three, and arbitrary continuous unit-sphere attaching maps, the genuine adjunction quotient of X and the coproduct of closed Euclidean unit balls is constructed with its quotient topology. The actual inclusion-induced fundamental-group homomorphism is bijective and is the underlying homomorphism of the displayed multiplicative equivalence. Mixed dimensions and the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":true,"formalizes":[{"title":"Algebraic Topology","identifier":"https://pi.math.cornell.edu/~hatcher/AT/AT..pdf#page=62","relationship":"formalizes"}]}