Signatures in algebra and topology

A collection of resources on the signatures of quadratic forms and their applications in algebra and the topology of manifolds.
The papers are arranged in reverse chronological order. There is naturally some overlap with Eight in algebra, topology and mathematical physics
Please email me at with suggestions for further inclusions.

  • E.Ghys and A.Ranicki Signatures in algebra, topology and dynamics (13.9.2016)
  • M.Bourrigan Quasimorphismes sur les groupes de tresses et forme de Blanchfield (2015)
  • C.Palmer Seifert matrices of braids with applications to isotopy and signatures (2015)
  • H. Benis-Sinaceur, L'oeuvre algebrique de Charles Francois Sturm, Collected works of Charles Francois Sturm.(French) Edited by Jean-Claude Pont in collaboration with Flavia Padovani. Birkh\"auser Verlag, Basel, 2009.
  • J.Collins An algorithm for computing the Seifert matrix of a link from a braid presentation (2007)
  • R.Brouzet, La double origine du groupe symplectique. Expo. Math. 22, 1 (2004), 55--82.
  • J.Barge and E.Ghys, Cocycles d'Euler et de Maslov. Math. Ann. 294, 2 (1992), 235--265.
  • H.Benis-Sinaceur, Deux moments dans l'histoire du theoreme d'algebre de Ch.F.Sturm. Rev. Histoire Sci. 41, 2 (1988), 99--132
  • M.F. Atiyah, The logarithm of the Dedekind \eta-function. Math. Ann. 278, 1-4 (1987), 335--380.
  • V.I. Arnold, Sturm theorems and symplectic geometry. Funktsional. Anal. i Prilozhen. 19, 4 (1985), 1--10, 95.
  • N.Bourbaki, Elements d'histoire des mathematiques. Masson, Paris, 1984.
  • W.Scharlau, Quadratic Reciprocity Laws J. Number Theory 4, 78--97 (1972)
  • V.I.Arnold, On a characteristic class entering into conditions of quantization. Funkcional. Anal. i Prilozen. 1 (1967), 1--14.
  • M.F.Atiyah and I.M.Singer, The index of elliptic operators on compact manifolds. Bull. Amer. Math. Soc. 69 (1963), 422--433.
  • V.A.Yakubovich and V.M.Starzhinskii, Linear differential equations with periodic coefficients. 1, 2, English translation, Halsted Press (1975)
  • P.Appell, Traite de mecanique rationnelle. Tome 5. Elements de calcul tensoriel. Applications geometriques et mecaniques. Gauthier-Villars, Paris 1955
  • G.Frobenius, Ueber das Traegheitsgesetz der quadratischen Formen. Journal fuer die reine und angewandte Mathematik 114 (1895), 187 -- 230.
  • S.Gundelfinger, Ueber die Transformation einer quadratischen Form in eine Summe von Quadraten, J. Reine Angew. Math. 91 (1881), 221--237.
  • C.W. Borchardt, , Bemerkung ueber die beiden vorstehenden Aufsaetze. Journal fuer die reine und angewandte Mathematik 53 (1857), 281--283.
  • J.J.Sylvester On a remarkable modification of Sturm's theorem Philosophical Magazine V (1853), 446--456.
  • J.J.Sylvester A demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares, Philosophical Magazine IV (1852), 138--142
  • J.J.Sylvester On a theory of the syzygetic relations of two rational integral functions, comprising an application to the theory of Sturm's functions, and that of the greatest algebraical common measure. Philosophical Transactions of the Royal Society of London CXLIII (1853), 407--548.
  • C.-W. Borchardt, Developpements sur l'equation a l'aide de laquelle on determine les inegalites seculaires du mouvement des planetes. Journal de mathematiques pures et appliquees 12 (1847), 50--67.