Open Research Index

Fundamental Groups of Arbitrary Two-Cell Attachments

Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

Palomar Registrypalomar/PALOMAR-2026-10-04-000011Oct 4, 2026math.ATscore 0

The full arbitrary-family two-cell attachment theorem for ordinary topological fundamental groups. For any path-connected topological space X, any basepoint, and any indexed family of continuous circle attaching maps, a genuine adjunction quotient is constructed from X and the coproduct of closed complex unit disks. The actual inclusion-induced fundamental-group homomorphism is surjective and its kernel is precisely the normal closure of the once-around attaching loops, transported along the specified basepoint paths. A quotient group isomorphism is proved compatible with the actual…

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