Matches in SemOpenAlex for { <https://semopenalex.org/work/W2031837204> ?p ?o ?g. }
Showing items 1 to 51 of
51
with 100 items per page.
- W2031837204 endingPage "177" @default.
- W2031837204 startingPage "177" @default.
- W2031837204 abstract "1. Introduction. A homotopy 3-cell is a compact, connected triangulated 3manifold whose boundary is a 2-sphere and whose fundamental group is trivial. The conjecture is true in dimension three if and only if every homotopy 3-cell is a 3-cell. If M is a 3-manifold, one says that the conjecture is true in M provided that every imbedded homotopy 3-cell in M is a 3-cell. Equivalently, one says that M is in PC (the Poincare Category). It will be shown in this paper that whenever any 3-manifold in PC is pasted to itself or to any other 3-manifold in PC across a disk, a sphere, or a projective plane, the resulting 3-manifold is in PC. Moreover, it will be shown that if pasting across any compact 2-manifold other than a disk, a sphere, or a projective plane always preserves membership in PC, then the conjecture is true. It follows from Theorem 1 of Moise [6] that if the underlying space of a homotopy 3-cell can be topologically imbedded in a 3-manifold M, then there is a piecewise linear imbedding of that homotopy 3-cell into any triangulation of M (and, of course, M can be triangulated). Therefore, if every piecewise linearly imbedded homotopy 3-cell in any particular triangulation of M is a 3-cell, then M is in PC. From now on, any manifold considered will be triangulated, and any map considered will be piecewise linear." @default.
- W2031837204 created "2016-06-24" @default.
- W2031837204 creator A5011936459 @default.
- W2031837204 date "1969-01-01" @default.
- W2031837204 modified "2023-10-18" @default.
- W2031837204 title "Manifolds in which the Poincaré conjecture is true" @default.
- W2031837204 cites W1507196244 @default.
- W2031837204 cites W1977010014 @default.
- W2031837204 cites W1988259761 @default.
- W2031837204 cites W2000041040 @default.
- W2031837204 cites W2018247246 @default.
- W2031837204 cites W2044876621 @default.
- W2031837204 cites W2075529902 @default.
- W2031837204 cites W2317299392 @default.
- W2031837204 cites W2468762483 @default.
- W2031837204 doi "https://doi.org/10.1090/s0002-9947-1969-0246302-0" @default.
- W2031837204 hasPublicationYear "1969" @default.
- W2031837204 type Work @default.
- W2031837204 sameAs 2031837204 @default.
- W2031837204 citedByCount "3" @default.
- W2031837204 crossrefType "journal-article" @default.
- W2031837204 hasAuthorship W2031837204A5011936459 @default.
- W2031837204 hasBestOaLocation W20318372041 @default.
- W2031837204 hasConcept C202444582 @default.
- W2031837204 hasConcept C2780990831 @default.
- W2031837204 hasConcept C33923547 @default.
- W2031837204 hasConcept C88221313 @default.
- W2031837204 hasConceptScore W2031837204C202444582 @default.
- W2031837204 hasConceptScore W2031837204C2780990831 @default.
- W2031837204 hasConceptScore W2031837204C33923547 @default.
- W2031837204 hasConceptScore W2031837204C88221313 @default.
- W2031837204 hasLocation W20318372041 @default.
- W2031837204 hasOpenAccess W2031837204 @default.
- W2031837204 hasPrimaryLocation W20318372041 @default.
- W2031837204 hasRelatedWork W1740107921 @default.
- W2031837204 hasRelatedWork W1980124684 @default.
- W2031837204 hasRelatedWork W2046365279 @default.
- W2031837204 hasRelatedWork W2463560742 @default.
- W2031837204 hasRelatedWork W2606009334 @default.
- W2031837204 hasRelatedWork W2793321405 @default.
- W2031837204 hasRelatedWork W2897153210 @default.
- W2031837204 hasRelatedWork W2950467121 @default.
- W2031837204 hasRelatedWork W3026358768 @default.
- W2031837204 hasRelatedWork W3106181326 @default.
- W2031837204 hasVolume "142" @default.
- W2031837204 isParatext "false" @default.
- W2031837204 isRetracted "false" @default.
- W2031837204 magId "2031837204" @default.
- W2031837204 workType "article" @default.