TY - JOUR
T1 - Stable maps of 3-manifolds into the plane and their quotient spaces
AU - Motta, Walter
AU - Porto, Paulo
AU - Saeki, Osamu
N1 - Funding Information:
The first author is partially supported by CNPg. The third author is partially supported by CCInt and FAPESP. 1991 Mathematics Subject Classification: 57R45.
PY - 1995/7
Y1 - 1995/7
N2 - 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.
AB - 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.
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U2 - 10.1112/plms/s3-71.1.158
DO - 10.1112/plms/s3-71.1.158
M3 - Article
AN - SCOPUS:84959802067
SN - 0024-6115
VL - s3-71
SP - 158
EP - 174
JO - Proceedings of the London Mathematical Society
JF - Proceedings of the London Mathematical Society
IS - 1
ER -