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  2. Euler characteristic - Wikipedia

    en.wikipedia.org/wiki/Euler_characteristic

    This equation, stated by Euler in 1758, [2] is known as Euler's polyhedron formula. [3] It corresponds to the Euler characteristic of the sphere (i.e. χ = 2 {\displaystyle \ \chi =2\ } ), and applies identically to spherical polyhedra .

  3. Euler characteristic of an orbifold - Wikipedia

    en.wikipedia.org/wiki/Euler_characteristic_of_an...

    In differential geometry, the Euler characteristic of an orbifold, or orbifold Euler characteristic, is a generalization of the topological Euler characteristic that includes contributions coming from nontrivial automorphisms.

  4. Local Euler characteristic formula - Wikipedia

    en.wikipedia.org/wiki/Local_Euler_characteristic...

    In the mathematical field of Galois cohomology, the local Euler characteristic formula is a result due to John Tate that computes the Euler characteristic of the group cohomology of the absolute Galois group G K of a non-archimedean local field K.

  5. Riemann–Hurwitz formula - Wikipedia

    en.wikipedia.org/wiki/Riemann–Hurwitz_formula

    Indeed, to obtain this formula, remove disjoint disc neighborhoods of the branch points from S and their preimages in S' so that the restriction of is a covering. Removing a disc from a surface lowers its Euler characteristic by 1 by the formula for connected sum, so we finish by the formula for a non-ramified covering.

  6. Euler class - Wikipedia

    en.wikipedia.org/wiki/Euler_class

    This can be seen intuitively in that the Euler class is a class whose degree depends on the dimension of the bundle (or manifold, if the tangent bundle): the Euler class is an element of () where is the dimension of the bundle, while the other classes have a fixed dimension (e.g., the first Stiefel-Whitney class is an element of ()).

  7. Eulerian number - Wikipedia

    en.wikipedia.org/wiki/Eulerian_number

    A tabulation of the numbers in a triangular array is called the Euler triangle or Euler's triangle. It shares some common characteristics with Pascal's triangle . Values of A ( n , k ) {\textstyle A(n,k)} (sequence A008292 in the OEIS ) for 0 ≤ n ≤ 9 {\textstyle 0\leq n\leq 9} are:

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