On handle decompositions and diffeomorphisms

Agoston, Max K.

doi:10.1090/s0002-9947-1969-0236938-5

Cited by 7 publications

(6 citation statements)

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“…Agoston's example [1] shows that some diffeomorphic minimal handle-decompositions cannot be isotopic; our example concerns, however, the ones which cannot be mutually diffeomorphic.…”

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confidence: 89%

“…Corollary 1 implies that two ordered minimal handle-decomposition on such a manifold become isotopic after some repeat of reorderings and handle-adding operations ; Agoston [1] has proved a weaker version of the uniqueness of the minimal handle-decomposition up to isotopy by using only the A-cobordism theorem, and he gave an example which showed that the torsion-freeness was indispensable to his uniqueness theorem and consequently to Corollary 1. We shall give another stronger counter-example, that is, an example of non-diffeomorphic minimal handle-decompositions in the appendix ( = §4).…”

Section: V) Has No Torsionsmentioning

confidence: 99%

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On the Minimal Ordered Morse Functions on Compact Simply-Connected Manifolds

Matumoto¹

1978

Publ. Res. Inst. Math. Sci.

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“…Agoston's example [1] shows that some diffeomorphic minimal handle-decompositions cannot be isotopic; our example concerns, however, the ones which cannot be mutually diffeomorphic.…”

mentioning

confidence: 89%

Section: V) Has No Torsionsmentioning

confidence: 99%

On the Minimal Ordered Morse Functions on Compact Simply-Connected Manifolds

Matumoto¹

1978

Publ. Res. Inst. Math. Sci.

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“…Let Mf: Vxlnx D"xl -> Vxlnx Dqxl be a map and define H:VxrxI->VxInxDQxI by H(x, t, s) = Mf(x, t,0, s). (H,Mf) is said to F-connect (/, ¿^) am/ (g, 9), or (/ #)~w.jr>(f, ^), if (1) Mf is a diffeomorphism, (2) ¿f(x, f, v, 0) = (&(x, t, v), 0), jT(x, t, v, l) = (^(x, f, v), 1),…”

Section: ) H(int (Vx In X /))Cint (Vx Inxd"x I)mentioning

confidence: 99%

“…A map/: Vx In ->• Vxlnx D" is called admissible if (1) /is an imbedding, (2) f(x, t) = (x, t, 0), for teJn~\ (3)f(Vx8In)=Vx8InxO, (4) f(Vx/n)eint (Vx7»x DP).…”

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Relative knots and tangential equivalences

Agoston¹

1969

Trans. Amer. Math. Soc.

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Levine has studied the groups, 6m,n, of knotted homotopy n-spheres in Sm. These groups can be interpreted as n-cobordism classes of certain ball pairs (Dm, Dn). In this paper we define a relativized version, 6m-n(Vk), of these groups, where Vk is a /¿-manifold. dm,n(V) is the group of n-cobordism classes of pairs (VxDm, VxDn), although in practice we find it convenient to give the formal definition in terms of maps rather than manifold pairs. Of course, 0m,n(point)= &m,n as a special case. We shall show that the groups 6m,n(V) and their framed analogues ff$-n(V) fit into exact sequences (see §3) generalizing those of [11] and [4]. Finally, we use these groups to obtain necessary and sufficient conditions under which a "partial" stable tangential homotopy equivalence /: M*-> Wn (i.e., /|[n/2]-skeleton is tangential) is actually a stable tangential homotopy equivalence (see §9). We rely heavily on the techniques of Rn will denote n-dimensional real vector space with unit cube /" and unit discFn-all with their natural orientations. Let Sn~1 = 8Dn, Jn-1 = dln-ln-1, where int X or X denotes the interior of X. Let Cl (X) be the closure of X. Z and Z, will mean the integers and cyclic group of order /, respectively.

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Deformation of Morse functions. I

Sharko¹

1989

Ukr Math J

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On handle decompositions and diffeomorphisms

Cited by 7 publications

References 4 publications

On the Minimal Ordered Morse Functions on Compact Simply-Connected Manifolds

On the Minimal Ordered Morse Functions on Compact Simply-Connected Manifolds

Relative knots and tangential equivalences

Deformation of Morse functions. I

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