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searching for Symplectic basis 6 found (14 total)

Arf invariant of a knot (739 words) [view diff] exact match in snippet view article find links to article

i } , i = 1 … g {\displaystyle \{a_{i},b_{i}\},i=1\ldots g} , is a symplectic basis for the intersection form on the Seifert surface, then Arf ⁡ ( K )

Topological recursion (4,377 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \Sigma } is a compact algebraic curve with a marking of a symplectic basis of cycles, x {\displaystyle x} is meromorphic and ω 0 , 1 = y d x {\displaystyle

Classical group (7,823 words) [view diff] exact match in snippet view article find links to article

ξ 1 η 1 + ξ 2 η 2 + ⋯ + ξ n η n , ( C ) Bilinear skew-symmetric in symplectic basis: φ ( x , y ) = ξ 1 η m + 1 + ξ 2 η m + 2 + ⋯ + ξ m η 2 m = n − ξ m

Arf invariant (3,422 words) [view diff] exact match in snippet view article find links to article

is certainly possible for m ≥ 4 {\displaystyle m\geq 4} ). Choose a symplectic basis x 1 , x 2 , … , x 2 g − 1 , x 2 g {\displaystyle x_{1},x_{2},\ldots

Translation surface (4,595 words) [view diff] exact match in snippet view article find links to article

γ k {\displaystyle \gamma _{1},\ldots ,\gamma _{k}} is as above a symplectic basis of this space. The stratum H ( α ) {\displaystyle {\mathcal {H}}(\alpha

Invariant convex cone (3,569 words) [view diff] exact match in snippet view article find links to article

diagonal. Scaling the orthonormal basis, it follows that there is a symplectic basis for R2n diagonalizing the original positive symmetric bilinear form