Bilinear and quadratic forms on torsion modules

Durfee, Alan H.

doi:10.1016/0001-8708(77)90002-0

Cited by 36 publications

(33 citation statements)

References 20 publications

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“…The implications (a.1) =⇒ (a.2) and (b.1) =⇒ (b.2) are straightforward. The converse (a.2) =⇒ (a.1) can be found in [Du,Corollary 4.2], in the case when f and g are non-degenerate, but the argument given applies in our case as well: simply decompose f (resp. g) as a direct sum of a 0-form and of a non-degenerate form on a summand of the lattice F (resp.…”

Section: Quadratic Forms On Abelian Groupsmentioning

confidence: 88%

“…Wall, M. Kneser, A. Durfee and others. We refer to [Du,§2] for the general construction and further references.…”

Section: Lemma 14 Let D Be a Nonzero Integer Assume That Either D mentioning

confidence: 99%

“…It is known that there always exists a form f : F × F → Z satisfying the hypothesis of Theorem 4 (see [Du,Corollary 4.2] or lemma 2.1, part (b), §2.2).…”

Section: Theorem 4 Let F : F × F → Z Be a Symmetric Bilinear Form Onmentioning

confidence: 99%

“…The surjectivity of the maps [Wa,Theorem 6]. See also [Du,Theorems 4.4 and 4.7] and [La] for generalizations. The surjectivity of M…”

Section: Quadratic Forms On Abelian Groupsmentioning

confidence: 99%

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Linking forms, reciprocity for Gauss sums and invariants of 3-manifolds

Deloup

1999

Trans. Amer. Math. Soc.

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Abstract. We study invariants of 3-manifolds derived from finite abelian groups equipped with quadratic forms. These invariants arise in Turaev's theory of modular categories and generalize those of H. Murakami, T. Ohtsuki and M. Okada. The crucial algebraic tool is a new reciprocity formula for Gauss sums, generalizing classical formulas of Cauchy, Kronecker, Krazer and Siegel. We use this reciprocity formula to give an explicit formula for the invariants and to generalize them to higher dimensions.

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Section: Quadratic Forms On Abelian Groupsmentioning

confidence: 88%

“…Wall, M. Kneser, A. Durfee and others. We refer to [Du,§2] for the general construction and further references.…”

Section: Lemma 14 Let D Be a Nonzero Integer Assume That Either D mentioning

confidence: 99%

“…It is known that there always exists a form f : F × F → Z satisfying the hypothesis of Theorem 4 (see [Du,Corollary 4.2] or lemma 2.1, part (b), §2.2).…”

Section: Theorem 4 Let F : F × F → Z Be a Symmetric Bilinear Form Onmentioning

confidence: 99%

“…The surjectivity of the maps [Wa,Theorem 6]. See also [Du,Theorems 4.4 and 4.7] and [La] for generalizations. The surjectivity of M…”

Section: Quadratic Forms On Abelian Groupsmentioning

confidence: 99%

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Linking forms, reciprocity for Gauss sums and invariants of 3-manifolds

Deloup

1999

Trans. Amer. Math. Soc.

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“…The precise nature of these invariants depends on whether n is even or odd. For the case n even Durfee [20] shows that for n > 3 and n ¤ 4; 8 there is an exact sequence…”

Section: Highly Connected Manifoldsmentioning

confidence: 99%

Highly connected manifolds with positive Ricci curvature

Boyer

Galicki

2006

Geom. Topol.

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We prove the existence of Sasakian metrics with positive Ricci curvature on certain highly connected odd dimensional manifolds. In particular, we show that manifolds homeomorphic to the 2k-fold connected sum of S 2n 1 S 2n admit Sasakian metrics with positive Ricci curvature for all k. Furthermore, a formula for computing the diffeomorphism types is given and tables are presented for dimensions 7 and 11.53C25; 57R55

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Symmetrische Bilinearformen auf endlichen Abelschen Gruppen

Barthel

1978

Geom Dedicata

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Bilinear and quadratic forms on torsion modules

Cited by 36 publications

References 20 publications

Linking forms, reciprocity for Gauss sums and invariants of 3-manifolds

Linking forms, reciprocity for Gauss sums and invariants of 3-manifolds

Highly connected manifolds with positive Ricci curvature

Symmetrische Bilinearformen auf endlichen Abelschen Gruppen

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