algebraic topology, the Euler class is a characteristic class of oriented, real vector bundles. Like other characteristic classes, it measures how "twisted"...

algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant...

Chern class is the first Chern class, which is an element of the second cohomology group of X. As it is the top Chern class, it equals the Euler class of...

mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique...

numbers, Pontryagin numbers, and the Euler characteristic. Given an oriented manifold M of dimension n with fundamental class [ M ] ∈ H n ( M ) {\displaystyle...

( M ) {\displaystyle \chi (M)} denotes the Euler characteristic of M {\displaystyle M} . The Euler class is defined as e ( Ω ) = 1 ( 2 π ) n Pf ⁡ ( Ω...

bundle is partially characterized by its Euler class, which is a degree n + 1 {\displaystyle n+1} cohomology class in the total space of the bundle. In the...

In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that, if n and a are coprime positive integers...

compact surfaces. His doctoral dissertation, "Discontinuous groups and the Euler class" (supervised by Morris W. Hirsch), characterizes discrete embeddings...

e(E)} denotes the Euler class of E {\displaystyle E} , and ⌣ {\displaystyle \smile } denotes the cup product of cohomology classes. As was shown by Shiing-Shen...

derivative is the virtual dimension. The localized Euler class of the pair (E,s) is a homology class with closed support on the zero set of the section...

manifold with non-zero Euler class e ( T X ) {\displaystyle e(TX)} , then applying the Thom isomorphism and dividing by the Euler class, the topological index...

vector bundle is a Chern class. A complex vector bundle is canonically oriented; in particular, one can take its Euler class. A complex vector bundle...

dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular...

cryptosystem. The Solovay–Strassen test is essentially an Euler–Jacobi probable prime test. Euler proved that for any odd prime number p and any integer...

space X determines a cohomology class on X, the Euler class χ(E) ∈ Hr(X,Z). Informally, the Euler class is the class of the zero set of a general section...

posthumously in 1873 by Carl Hierholzer. This is known as Euler's Theorem: A connected graph has an Euler cycle if and only if every vertex has an even number...

fundamental class of Sn and χ the Euler characteristic. If we work on a manifold of dimension n, then any product of Stiefel–Whitney classes of total degree n...

resemble the Euler factors of an Euler product. Euler systems can be used to construct annihilators of ideal class groups or Selmer groups, thus giving...

logarithm, also commonly written as ln(x) or loge(x). Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually...

cohomology class e called the Euler class of the bundle. Discussion of the sequence is clearest with de Rham cohomology. There cohomology classes are represented...

In Itô calculus, the Euler–Maruyama method (also simply called the Euler method) is a method for the approximate numerical solution of a stochastic differential...

Poincaré duality, Euler class of Sphere bundles, Thom classes and Thom isomorphism, and more. Milnor, John. Characteristic classes. is another standard...

an Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick...

as by Christian Weise in 1712 (Nucleus Logicoe Wiesianoe) and Leonhard Euler (Letters to a German Princess) in 1768. The idea was popularised by Venn...

invariant of an oriented bundle is the Euler class. The multiplication (that is, cup product) by the Euler class of an oriented bundle gives rise to a...

Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) is a simplification of the linear theory of elasticity which...

criterion dates from a 1748 paper by Leonhard Euler. The proof uses the fact that the residue classes modulo a prime number are a field. See the article...

In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains...

In mathematics, the Euler numbers are a sequence En of integers (sequence A122045 in the OEIS) defined by the Taylor series expansion 1 cosh ⁡ t = 2 e...