Quadratic Spherical Maps

  • Takashi Ono
Part of the The University Series in Mathematics book series (USMA)


Let K be an infinite field of characteristic #2. For vector spaces X, Y over K of finite dimension, we defined a quadratic mapf: X→ Y by the following conditions :
$$f(ax) = {a^2}f(x),a \in K,x \in X$$
$$(x,y) \mapsto \frac{1}{2}[f(x + y) - f(x) - f(y)],x,y \in XS$$
is bilinear [see (1.2) and (1.3)]. We denoted by Q(X, Y) the set of all such maps. In what follows, we assume that X, Y are both nonsingular quadratic spaces with quadratic forms q x , q Y , respectively, and there are x∈X, y∈Y such that q x (x) = qy(y) = 1. Therefore the unit spheres S x , S Y are nonempty:
$${S_X} = \{ x \in X;{q_X}(X) = 1\} ,{S_Y} = \{ y \in Y;{q_Y}(y) = 1\} $$


Quadratic Form Orthogonal Basis Homotopy Theory Infinite Field Witt Theorem 
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Copyright information

© Takashi Ono 1994

Authors and Affiliations

  • Takashi Ono
    • 1
  1. 1.The Johns Hopkins UniversityBaltimoreUSA

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