Equivariant index theorem information

In differential geometry, the equivariant index theorem, of which there are several variants, computes the (graded) trace of an element of a compact Lie...

replace ordinary K-theory in the index theorem with equivariant K-theory. For trivial groups G this gives the index theorem, and for a finite group G acting...

holds if every rule satisfies the following two conditions: the rule is equivariant in the sense of nominal logic, that is to say that its validity is unchanged...

over F, equipped with representations φ and ψ of a group G, then an equivariant map from V to W is a linear map α: V → W such that α ( g ⋅ v ) = g ⋅...

subgroup of index p. The focal subgroup theorem relates several lines of investigation in finite group theory: normal subgroups of index a power of p...

Kampen theorem Homotopy excision theorem Freudenthal suspension theorem (a corollary of the excision theorem) Landweber exact functor theorem Dold–Kan...

representations, the Frobenius reciprocity theorem states that, given representations σ of H and ρ of G, the space of H-equivariant linear maps from σ to Res(ρ) has...

allows expressing the fundamental theorem of calculus, the divergence theorem, Green's theorem, and Stokes' theorem as special cases of a single general...

Mathematics portal Characterizations of the category of topological spaces Equivariant topology List of algebraic topology topics List of examples in general...

} . This is now known as the Hirzebruch signature theorem (or sometimes the Hirzebruch index theorem). The fact that L 2 {\displaystyle L_{2}} is always...

{\text{GL}}(W)} ). Then a tensor of type ρ {\displaystyle \rho } is an equivariant map T : F → W {\displaystyle T:F\to W} . Equivariance here means that...

map and equivariant cohomology". Topology. 23 (1): 1–28. doi:10.1016/0040-9383(84)90021-1. Duistermaat, J. J (1976-08-01). "On the Morse index in variational...

Richard Melrose and Isadore Singer, on the fractional analytic index and on the index theorem for projective families of elliptic operators. His current work...

{L}}(\alpha )=\sup _{\theta :\alpha =g(\theta )}L(\theta ).\,} The MLE is also equivariant with respect to certain transformations of the data. If y = g ( x ) {\displaystyle...

(such as a principal bundle), bundle morphisms are also required to be G-equivariant on the fibers. This means that φ : E → F {\displaystyle \varphi :E\to...

algebra of a Lie algebra. category of representations Representations and equivariant maps between them form a category of representations. character 1.  A...

deleted tangent bundle TM \ {0}) it is enough that the connection be equivariant under positive rescalings: it need not be linear. That is, (cf. Ehresmann...

( ⋅ ) {\displaystyle (\cdot )} is a K × {\displaystyle K^{\times }} -equivariant group homomorphism. As a consequence, the map above induces a surjective...