Examples of 'euler characteristic' in a sentence
Meaning of "euler characteristic"
The Euler characteristic is a mathematical concept used in topology to describe the geometric shape of an object. It is a number that represents the relationship between the number of vertices, edges, and faces of a polyhedron or a graph
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- The sum of even-dimensional Betti numbers minus the sum of odd-dimensional ones.
How to use "euler characteristic" in a sentence
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euler characteristic
Euler characteristic constant under barycentric subdivision.
It can compute the Euler characteristic of an orbifold.
Euler characteristic of a sheaf.
This follows from a straightforward Euler characteristic argument.
Let be the Euler characteristic of a closed surface.
This number is now called the Euler characteristic.
A version of Euler characteristic used in algebraic geometry is as follows.
It is either a noncompact topological space or a compact space with a zero Euler characteristic.
The Euler characteristic is a topological invariant for surfaces.
Thus closed surfaces are classified up to diffeomorphism by their Euler characteristic and orientability.
The Euler characteristic can then be defined as the alternating sum.
Care has to be taken to use the correct Euler characteristic for the polyhedron.
The Euler characteristic of the Möbius strip is zero.
Examples of such are the fundamental groups of closed surfaces of negative Euler characteristic.
A test of Gaussianity based on the Euler characteristic of excursion sets.
See also
The Euler characteristic of an elliptic space X is nonnegative.
Betti numbers and the Euler characteristic.
The graded Euler characteristic of knot Floer homology is the Alexander polynomial.
The Jones polynomial is described as the Euler characteristic for this homology.
Hence the Euler characteristic of this category is 1.
These are topological tori, with Euler characteristic of zero.
In this way, the Euler characteristic can be viewed as a generalisation of cardinality ; see.
So, this is called the Euler characteristic.
The concept of Euler characteristic of a bounded finite poset is another generalization, important in combinatorics.
In particular, the Euler characteristic is.
Thus 2 is a topological invariant of the sphere, called its Euler characteristic.
See also Euler characteristic.
The one that is homogenous of degree 0 is the Euler characteristic.
The Euler characteristic of an orbifold can be read from its Conway symbol, as follows.
This explains why convex polyhedra have Euler characteristic 2.
What results is that the Euler characteristic ( of a coherent sheaf ) is something reasonably computable.
In algebraic topology, Chi is used to represent the Euler characteristic of a surface.
Results for the Euler characteristic lead to corrected p-values for each voxel hypothesis.
Another, more topological example of an intrinsic property of a manifold is the Euler characteristic.
The entire HOMFLY-PT polynomial is the Euler characteristic of a triply graded link homology theory.
Subtracting the sum of these values from 2 gives the Euler characteristic.
While every manifold has an integer Euler characteristic, an orbifold can have a fractional Euler characteristic.
Euler was first to explore topology, proving theorems about the Euler characteristic.
The Euler characteristic of any plane connected graph G is 2.
Uniform tilings on the plane correspond to a torus topology, with Euler characteristic of zero.
Euler characteristic The five Platonic solids have an Euler characteristic of 2.
Homology theory can be said to start with the Euler polyhedron formula, or Euler characteristic.
Its Euler characteristic is 0, by the product property.
The five Platonic solids have an Euler characteristic of 2.
The boundary 's Euler characteristic is 0 for even m and 2 for odd m.
Planar graphs, graphs on a surface, Euler characteristic.
It follows that the Euler characteristic of the n-torus is 0 for all n.
Otherwise, the order is 2 divided by the Euler characteristic.
The Euler characteristic of any closed odd-dimensional manifold is also 0.
However, it had an Euler characteristic of 0.
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