On special generic maps of simply connected 2n-manifolds into R3

Sakuma, Kazuhiro

doi:10.1016/0166-8641(93)90024-8

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Introduction2

] and R : I → I Is The Reflection Defined By R(t) = −T Then1

Manifolds With Free Fundamental Groups Admitting a Special1

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Cited by 25 publications

(26 citation statements)

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“…Remark 3.7. By using a formula of Rohlin [25] and Guillou-Marin [14], Sakuma [35] has shown that for a fold map f :…”

Section: ] and R : I → I Is The Reflection Defined By R(t) = −T Thenmentioning

confidence: 99%

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Fold maps on 4-manifolds

Saeki¹

2003

Comment. Math. Helv.

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“…Remark 3.7. By using a formula of Rohlin [25] and Guillou-Marin [14], Sakuma [35] has shown that for a fold map f :…”

Section: ] and R : I → I Is The Reflection Defined By R(t) = −T Thenmentioning

confidence: 99%

“…In [26], the author has shown that no 4-manifold M that has the integral homology of CP 2 admits a fold map into R 3 , by using Sakuma's modulo four formula [35], which is a consequence of Rohlin's result [25,14] peculiar to 4-dimensions. Such a phenomenon was not expected in view ofÈliasberg's result and turned our attention to the problem again.…”

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confidence: 99%

Fold maps on 4-manifolds

Saeki¹

2003

Comment. Math. Helv.

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“…Note that the above theorem for the trivial fundamental group has been proved in [31] and [32] (see also [34]). Furthermore, in the case where M is orientable of dimension four and the quotient space W f is homeomorphic to a boundary connected sum of some solid tori, a similar result has been obtained in [20].…”

Section: Manifolds With Free Fundamental Groups Admitting a Specialmentioning

confidence: 99%

“…This is a generalization of results in [34], [31], [32], where simply connected manifolds admitting special generic maps into R 3 have been studied. Using this classification theorem, we give some examples of pairs of homeomorphic smooth 4-manifolds (M 1 , M 2 ) such that M 1 admits a special generic map into R 3 while M 2 does not.…”

Section: Introductionmentioning

confidence: 99%

“…These results imply that if a manifold of dimension greater than or equal to three admits a special generic map into R 2 , then its fundamental group must be a free group. Note also that Sakuma [34] and Saeki [31], [32] have studied special generic maps of simply connected manifolds into R 3 . In this paper, we consider special generic maps of nonsimply connected manifolds into R 3 in general and give various new results about the global topology of such maps.…”

Section: Introductionmentioning

confidence: 99%

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On special generic maps into R³

Saeki

Sakuma

1998

Pacific J. Math.

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Let f : M → R p be a smooth map of a closed n-dimensional manifold M into R p (n ≥ p) which has only definite fold singularities as its singular points. Such a map is called a special generic map, which was first defined by Burlet and de Rham for (n, p) = (3, 2) and later extended to general (n, p) by Porto, Furuya, Sakuma and Saeki. In this paper, we study the global topology of such maps for p = 3 and give various new results, among which are a splitting theorem for manifolds admitting special generic maps into R 3 and a classification theorem of 4-and 5-dimensional manifolds with free fundamental groups admitting special generic maps into R 3 . Furthermore, we study the topological structure of the surfaces which arise as the singular set of a special generic map into R 3 on a given manifold.

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