-
notion of
pushforward in
mathematics is "dual" to the
notion of pullback, and can mean a
number of
different but
closely related things.
Pushforward (differential)...
- In
differential geometry,
pushforward is a
linear approximation of
smooth maps (formulating manifold) on
tangent spaces.
Suppose that φ : M → N {\displaystyle...
- In
measure theory, a
pushforward measure (also
known as push forward, push-forward or
image measure) is
obtained by
transferring ("pushing forward") a...
- In
algebraic topology, the
pushforward of a
continuous function f {\displaystyle f} : X → Y {\displaystyle X\rightarrow Y}
between two
topological spaces...
- In the
mathematical field of
measure theory, an
outer measure or
exterior measure is a
function defined on all
subsets of a
given set with
values in the...
- The
pushforward is
harder to
define formally. For simplicity, fix
Lebesgue measures on U {\displaystyle U} and V . {\displaystyle V.} The
pushforward can...
-
tangent bundle, the
pushforward is a
vector bundle homomorphism: F ∗ : T M → T N . {\displaystyle F_{*}:TM\to TN.} The dual to the
pushforward is the pullback...
- can
define a new
sheaf f∗F on Y,
called the
direct image sheaf or the
pushforward sheaf of F
along f, such that the
global sections of f∗F is
given by...
- {\displaystyle \phi } is a diffeomorphism, then the pullback,
together with the
pushforward, can be used to
transform any
tensor field from N {\displaystyle N} to...
- but
related processes:
precomposition and fiber-product. Its dual is a
pushforward.
Precomposition with a
function probably provides the most elementary...
