Open Research Index

Fundamental Groups of Arbitrary Higher-Cell Attachments

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

Palomar Registrypalomar/PALOMAR-2026-10-05-000001Oct 5, 2026math.ATscore 0

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…

SourceRepositoryJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/palomar/PALOMAR-2026-10-05-000001
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-05-000001/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-05-000001/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'