Ε-quadratic formIn mathematics, specifically the theory of quadratic forms, an ε-quadratic form is a generalization of quadratic forms to skew-symmetric settings and to *-rings; ε = ±1, accordingly for symmetric or skew-symmetric. They are also called -quadratic forms, particularly in the context of surgery theory. There is the related notion of ε-symmetric forms, which generalizes symmetric forms, skew-symmetric forms (= symplectic forms), Hermitian forms, and skew-Hermitian forms.
Arf invariantIn mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Turkish mathematician when he started the systematic study of quadratic forms over arbitrary fields of characteristic 2. The Arf invariant is the substitute, in characteristic 2, for the discriminant for quadratic forms in characteristic not 2. Arf used his invariant, among others, in his endeavor to classify quadratic forms in characteristic 2.
Genus of a multiplicative sequenceIn mathematics, a genus of a multiplicative sequence is a ring homomorphism from the ring of smooth compact manifolds up to the equivalence of bounding a smooth manifold with boundary (i.e., up to suitable cobordism) to another ring, usually the rational numbers, having the property that they are constructed from a sequence of polynomials in characteristic classes that arise as coefficients in formal power series with good multiplicative properties.
Hirzebruch signature theoremIn differential topology, an area of mathematics, the Hirzebruch signature theorem (sometimes called the Hirzebruch index theorem) is Friedrich Hirzebruch's 1954 result expressing the signature of a smooth closed oriented manifold by a linear combination of Pontryagin numbers called the L-genus. It was used in the proof of the Hirzebruch–Riemann–Roch theorem. The L-genus is the genus for the multiplicative sequence of polynomials associated to the characteristic power series The first two of the resulting L-polynomials are: (for further L-polynomials see or ).
Classe de PontriaguineEn mathématiques, les classes de Pontriaguine sont des classes caractéristiques associées aux fibrés vectoriels réels, nommées d'après Lev Pontriaguine. Les classes de Pontriaguine appartiennent aux groupes de cohomologie de degré un multiple de quatre. Soit E un fibré vectoriel réel au-dessus de M. La k-ième classe de Pontriaguine pk(E) est définie par : pk(E) = pk(E, Z) = (−1)k c2k(E ⊗ C) ∈ H4k(M, Z), où c2k(E ⊗ C) est la 2k-ième classe de Chern du complexifié E ⊗ C = E ⊕ iE de E ; H4k(M, Z) est le 4k-ième groupe de cohomologie de M à coefficients entiers.
CobordismeEn topologie différentielle, le cobordisme est une relation d'équivalence entre variétés différentielles compactes. Deux variétés compactes M et N sont dites cobordantes ou en cobordisme si leur réunion disjointe peut être réalisée comme le bord d'une variété à bord compacte L. On dit alors que cette variété L est un cobordisme entre M et N, ou bien que L réalise un cobordisme entre M et N. L'existence d'un tel cobordisme implique que M et N soient de même dimension.
