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searching for Bundle map 15 found (26 total)

alternate case: bundle map

Orientation of a vector bundle (657 words) [view diff] exact match in snippet view article find links to article

vector space Ex and one demands that each trivialization map (which is a bundle map) ϕ U : π − 1 ( U ) → U × R n {\displaystyle \phi _{U}:\pi ^{-1}(U)\to

Pullback (differential geometry) (2,251 words) [view diff] exact match in snippet view article

^{*}TN} . The transpose of ϕ ∗ {\displaystyle \phi _{*}} is therefore a bundle map from ϕ ∗ T ∗ N {\displaystyle \phi ^{*}T^{*}N} to T ∗ M {\displaystyle

Plumbing (mathematics) (985 words) [view diff] exact match in snippet view article

M B 4 k → ξ {\displaystyle b:\nu _{M_{B}^{4k}}\rightarrow \xi } is a bundle map from the stable normal bundle of the Milnor manifold to a certain stable

Vector-valued differential form (2,332 words) [view diff] exact match in snippet view article find links to article

{f}}\leftrightarrow f} . Example: Let E be the tangent bundle of M. Then identity bundle map idE: E →E is an E-valued one form on M. The tautological one-form is a

Section (fiber bundle) (1,138 words) [view diff] exact match in snippet view article

Right inverse of a fiber bundle map

Complex vector bundle (736 words) [view diff] exact match in snippet view article find links to article

structure, the complex structure. By definition, a complex structure is a bundle map between a real vector bundle E {\displaystyle E} and itself: J : E → E

Pullback (category theory) (2,058 words) [view diff] exact match in snippet view article

example of a pullback comes from the theory of fiber bundles: given a bundle map π : E → B and a continuous map f : X → B, the pullback (formed in the

Clifford module bundle (356 words) [view diff] exact match in snippet view article find links to article

are called spinors on M. Given a spinor bundle S(M) there is a natural bundle map C ℓ ( T ∗ M ) ⊗ S ( M ) → S ( M ) {\displaystyle C\ell (T^{*}M)\otimes

Canonical bundle (2,548 words) [view diff] exact match in snippet view article find links to article

generated: the symmetric powers of the space of sections of the canonical bundle map onto the sections of its tensor powers. This implies for instance the

Connection (principal bundle) (3,436 words) [view diff] exact match in snippet view article

P} . It follows that ω {\displaystyle \omega } determines uniquely a bundle map v : T P → V {\displaystyle v:TP\rightarrow V} which is the identity on

Spin structure (4,373 words) [view diff] exact match in snippet view article find links to article

action of the spin group Spin(n), by which we mean that there exists a bundle map ϕ {\displaystyle \phi } : PSpin(E) → PSO(E) such that ϕ ( p g ) = ϕ (

Courant algebroid (1,583 words) [view diff] exact match in snippet view article find links to article

\langle \cdot ,\cdot \rangle :E\times E\to M\times \mathbb {R} } , and a bundle map ρ : E → T M {\displaystyle \rho :E\to TM} (called anchor) subject to the

Musical isomorphism (5,000 words) [view diff] exact match in snippet view article find links to article

\alpha ^{\sharp }} is called the sharp of α. The sharp map is a smooth bundle map ♯ : T ∗ M → T M {\displaystyle \sharp :\mathrm {T} ^{*}M\to \mathrm {T}

Glossary of algebraic geometry (12,496 words) [view diff] exact match in snippet view article find links to article

(typically X' is assumed to be flat). degeneracy locus Given a vector-bundle map f : E → F {\displaystyle f:E\to F} over a variety X (that is, a scheme

Surgery exact sequence (3,121 words) [view diff] exact match in snippet view article find links to article

(that means f ∗ ( [ M ] ) = [ X ] {\displaystyle f_{*}([M])=[X]} ), and a bundle map b : T M ⊕ ε k → ξ {\displaystyle b\colon TM\oplus \varepsilon ^{k}\to