In mathematics, more specifically in
topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
, the equivariant stable homotopy theory is a subfield of
equivariant topology
In mathematics, equivariant topology is the study of topological spaces that possess certain symmetries. In studying topological spaces, one often considers continuous maps f: X \to Y, and while equivariant topology also considers such maps, the ...
that studies a
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...
with
group action
In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism ...
instead of a space with group action, as in
stable homotopy theory
In mathematics, stable homotopy theory is the part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the F ...
. The field has become more active recently because of its connection to
algebraic K-theory
Algebraic ''K''-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called ''K''-groups. These are groups in the sense ...
.
See also
*
Equivariant K-theory
*
G-spectrum In algebraic topology, a G-spectrum is a spectrum with an action of a (finite) group.
Let ''X'' be a spectrum with an action of a finite group ''G''. The important notion is that of the homotopy fixed point set X^. There is always
:X^G \to X^,
a ma ...
(spectrum with an action of an (appropriate) group ''G'')
References
External links
Creating Equivariant Stable Homotopy Theory
Homotopy theory
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