The Khovanov bracket is a chain complex of graded vector spaces whose graded value of this kind is the Jones polynomial.The sum of the indices of the critical points of a continuous tangent vector Âfield with isolated singularities on a compact,connected, orientable surface is given by this number. The Riemann-Hurwitz formula describes the relationship between thisvalue for two different surfaces when one is a covering space of the other. For a given CW-complex, this n
The Khovanov bracket is a chain complex of graded vector spaces whose graded value of this kind is the Jones polynomial.The sum of the indices of the critical points of a continuous tangent vector Âfield with isolated singularities on a compact,connected, orientable surface is given by this number. The Riemann-Hurwitz formula describes the relationship between thisvalue for two different surfaces when one is a covering space of the other. For a given CW-complex, this number is deÂfined asthe alternating sum of the ranks of the nth homology groups, or equivalently as the alternating sum of the number of n-cells.The global integral of the Gaussian curvature of an oriented, connected, closed, compact, regular space is given by two pi timesthis number. For a polyhedron, this number can be calculated by taking the number of vertices and subtracting the numberof edges then adding the number of faces. For a convex polyhedron this number is always equal to two. For 10 points, namethis number which describes the shape of a topological space, named for a Swiss mathematician.
The Khovanov bracket is a chain complex of graded vector spaces whose graded value of this kind is the Jones polynomial.
: Euler characteristic [prompt on "chi", accept Euler-Poincare characteristic]