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...

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...

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...

( 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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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

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...

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

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...

importance in showing the practical feasibility of the RSA cryptosystem. Euler proved that for any odd prime number p and any integer a, a ( p − 1 ) /...

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

) {\displaystyle \mathbb {G} (1,3)} . In order to get the Euler class, the total Chern class of T ∗ {\displaystyle T^{*}} must be computed, which is given...

obstruction bundle, and then realizing the GW invariant as the integral of the Euler class of the obstruction bundle. Making this idea precise requires significant...

An Euler diagram (/ˈɔɪlər/, OY-lər) is a diagrammatic means of representing sets and their relationships. They are particularly useful for explaining...

defined by cupping with the Euler class e ( E ) {\displaystyle e({\mathcal {E}})} . In this case it is given by the top chern class of E {\displaystyle {\mathcal...

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

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...

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...