Stable maps of 3-manifolds into the plane and their quotient spaces

Walter Motta, Paulo Porto, Osamu Saeki

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


We study stable maps f: M → R2of closed orientable 3-manifolds M into the plane using their quotient spaces, which are defined to be the spaces of the connected components of f-fibres and which are known to be 2-dimensional polyhedra. We show that every 3-manifold admits a stable map whose quotient space is homeomorphic to that of a stable map of S3We also deduce a Morse-type inequality for stable maps, which implies that there is no universal stable map of S3in the above sense. Certain moves in the quotient spaces corresponding to generic homotopies of stable maps are also studied.

Original languageEnglish
Pages (from-to)158-174
Number of pages17
JournalProceedings of the London Mathematical Society
Issue number1
Publication statusPublished - Jul 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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