Cohomologie-Operationen und charakteristische Klassen

Atiyah, Michael; Hirzebruch, Friedrich

doi:10.1007/bf01180171

Cited by 49 publications

(29 citation statements)

References 19 publications

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“…The material in this paper is an expanded and self-contained version of the purely number-theoretical part of [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. § 1.…”

Section: ~1-1 ~"---1 "mentioning

confidence: 99%

Higher dimensional dedekind sums

Zagier

1973

Math. Ann.

121

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“…The material in this paper is an expanded and self-contained version of the purely number-theoretical part of [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. § 1.…”

Section: ~1-1 ~"---1 "mentioning

confidence: 99%

Higher dimensional dedekind sums

Zagier

1973

Math. Ann.

121

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“…Indeed the last factor c * The right hand side is a linear combination of the Pontrjagin numbers of M with rational coefficients. These rational coefficients have odd denominators by a theorem of Atiyah and Hirzebruch saying that the coefficients of the L class have this property, (see [2] or lemma 1.5.2 in [10]), and the Pontrjagin numbers of M n are even by Stong's theorem. Since the signature is an integer it must be an even number.…”

Section: Now Using the Equality L((mmentioning

confidence: 99%

On the multiple points of immersions in Euclidean spaces

Szűcs

1998

Proc. Amer. Math. Soc.

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Abstract. Given a self-transverse immersion of a closed, oriented manifold in a euclidean space and a natural number i we compute the oriented cobordism class of the manifold of i-tuple points. §0. IntroductionLet f : M n → R n+k be a generic smooth immersion of a closed smooth manifold M n in the euclidean space R n+k and let ∆ i (f ) denote the manifold of i-fold points in the image. The manifold ∆ i (f ) is immersed in R n+k by a (non-generic) immersion g i ; the image of the non-multiple points of g i is the set of those points in R n+k which have exactly i preimages.The aim of this paper is to investigate the topological characteristics of these manifolds ∆ i (f ). In particular we compute their signatures and more generally all their Pontrjagin numbers, show that in many cases they have even Euler characteristics, and investigate whether the cobordism class of the manifold M n determines their cobordism class or not. It turns out that when the multiplicity i is odd, then the oriented cobordism class [∆ i (f )] of ∆ i (f ) is determined by the oriented cobordism class of M n , while for i even the oriented cobordism class [∆ i (f )] is independent of the cobordism class of M n . §1. Formulation of the resultsThe prototype of this kind of result is that of Banchoff:

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“…The basic technique in these proofs can be found already in work of Atiyah and Hirzebruch [2]. Working in the category of finite CW-complexes we set…”

Section: Proposition 27 the Polynomialmentioning

confidence: 99%