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homotopy groups and
cohomotopy groups,
important invariants in
algebraic topology. In practice,
there are
technical difficulties in
using homotopies with...
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homotopies that are
constant on the
basepoint of the sphere. Equivalently,
define π n ( X ) {\displaystyle \pi _{n}(X)} to be the
group of
homotopy classes...
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between them.
Regular homotopy for
immersions is
similar to
isotopy of embeddings: they are both
restricted types of
homotopies.
Stated another way, two...
- In the
mathematical field of
algebraic topology, the
homotopy groups of
spheres describe how
spheres of
various dimensions can wrap
around each other....
- In mathematics,
homotopy theory is a
systematic study of
situations in
which maps can come with
homotopies between them. It
originated as a
topic in algebraic...
- . Two
functions f , g : A → B {\displaystyle f,g:A\rightarrow B} are
homotopies by
pointwise identification:: 2.4.1 f ∼ g :≡ ∏ x : A f ( x ) = g ( x...
- the
homotopy extension property indicates which homotopies defined on a
subspace can be
extended to a
homotopy defined on a
larger space. The
homotopy extension...
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branch of mathematics, a
homotopy sphere is an n-manifold that is
homotopy equivalent to the n-sphere. It thus has the same
homotopy groups and the same homology...
- In
algebraic topology, a
simplicial homotopy is an
analog of a
homotopy between topological spaces for
simplicial sets. Precisely,pg 23 if f , g : X →...
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mathematical visualization: Half-way models:
these consist of very
special homotopies. This is the
original method,
first done by
Shapiro and
Phillips via Boy's...
