In mathematics, more specifically in
topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...
, 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 i ...
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. 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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