In mathematics, the fundamental class is a homology class [M] associated to a connected orientable compact manifold of dimension n, which corresponds...

specifically enumerative geometry and symplectic geometry, the virtual fundamental class [ X ] vir ∈ H ∗ ( X ) {\displaystyle [X]^{\text{vir}}\in H_{*}(X)}...

H_{n}(M;R)} as the fundamental class. For a closed R {\displaystyle R} -orientable n-manifold M {\displaystyle M} with fundamental class [ M ] {\displaystyle...

is compatible with orientation, i.e. which maps the fundamental class of M to the fundamental class of N, then D N = f ∗ ∘ D M ∘ f ∗ , {\displaystyle D_{N}=f_{*}\circ...

that the most fundamental characteristic classes known at that time (the Stiefel–Whitney class, the Chern class, and the Pontryagin classes) were reflections...

B\mathbb {G} _{m}} , the class h 0 = [ P n ] {\displaystyle h^{0}=[\mathbb {P} ^{n}]} , any n, may be thought of as the fundamental class of B G m {\displaystyle...

C P n ) {\displaystyle \xi \in H^{2}({\mathbb {C} }P^{n})} be the fundamental class of the hyperplane section. From multiplicativity and the Euler exact...

mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained...

geometry, the Chern classes are characteristic classes associated with complex vector bundles. They have since become fundamental concepts in many branches...

has an integer value (0, 1, 2, ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have half...

}}H_{n-i}(X,R)} is defined by cap product with the fundamental class of X. Although cohomology is fundamental to modern algebraic topology, its importance was...

denotes a 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...

The Fundamental Rights in India enshrined in part III (Article 12–35) of the Constitution of India guarantee civil liberties such that all Indians can...

addition, this glossary also includes some concepts (e.g., virtual fundamental class) in intersection theory that appear in symplectic geometry as they...

a fundamental class [ M ] ∈ H n B M ( M ) . {\displaystyle [M]\in H_{n}^{BM}(M).} If the manifold M has a triangulation, then its fundamental class is...

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every...

endpoints. The fundamental groupoid Π(X), or Π1(X), assigns to each ordered pair of points (p, q) in X the collection of equivalence classes of continuous...

development of SOM in 1997, it is still a fundamental framework for OS/2. The OS/2 version of Object REXX includes classes to support SOM and WPS. These are included...

the 1970s with generic uses of languages for specifying combinatorial classes and their generating functions, as found in works by Foata and Schützenberger...

of its points, i.e., the integral of the cohomology class 1 against the virtual fundamental class. The Donaldson–Thomas invariant is a holomorphic analogue...

Spurs in the National Basketball Association (NBA). Nicknamed "the Big Fundamental", he is widely considered the greatest power forward of all time and...

commutative diagram, where the right vertical map is cap product with the fundamental class of X in Borel–Moore homology: Pic ⁡ ( X ) ⟶ H 2 ( X , Z ) ↓ ↓ Cl ⁡...

denotes the k {\displaystyle k} -th Pontryagin class and [ M ] {\displaystyle [M]} the fundamental class of M {\displaystyle M} . Pontryagin numbers are...

algebraic number theory, the Shafarevich–Weil theorem relates the fundamental class of a Galois extension of local or global fields to an extension of...

d=-12,-16,-27,-28.} Thus, the even discriminants of class number 1, fundamental and non-fundamental (Gauss's original question) are: d = − 4 , − 8 , −...

Intersection cohomology Lusternik–Schnirelmann category Poincaré duality Fundamental class Applications Jordan curve theorem Brouwer fixed point theorem Invariance...

for instance, the top dimensional cell is unique (it represents the fundamental class), and corresponds to the longest element of a Coxeter group. The number...

expression for the fundamental class of a degeneracy locus (or determinantal variety) of a morphism of vector bundles in terms of Chern classes. Giambelli's...

about representation theory is that cuspidal representations are the fundamental class of objects, from which other representations may be constructed by...

A character class is a fundamental part of the identity and nature of characters in the Dungeons & Dragons role-playing game. A character's capabilities...