zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Mapping three-manifolds into the plane. I. (English) Zbl 0586.57018
In this paper the authors study global properties of stable maps of compact three manifolds into the plane. Let M be a compact orientable 3- manifold without boundary. For a stable map f:M 2 , let W f be the quotient of M obtained by identifying two points of M if they are in the same connected component of the same fibre of f. Let q:MW f be the quotient map and f ¯:W f 2 be defined by f=f ¯q. For any stable map f:M 2 , they show that the map f ¯:W f 2 can be lifted to a map g:W f 4 with pleasant properties. By this result, they also give a sufficient condition for existence of a lifting of f:M 2 to an immersion F of M into 4 (Theorem 2.2). This result is a very interesting result in the same direction as A. Haefliger [Ann. Inst. Fourier 10, 47-60 (1960; Zbl 0095.377)] and Y. Saito [J. Math. Kyoto Univ. 1, 425-455 (1962; Zbl 0201.563)].
Reviewer: S.Izumiya

57R45Singularities of differentiable mappings
58C25Differentiable maps on manifolds (global analysis)
58K99Theory of singularities and catastrophe theory
57R42Immersions (differential topology)
57N10Topology of general 3-manifolds