Struct FredholmModule 

pub struct FredholmModule {
    pub algebra: String,
    pub hilbert_space: String,
    pub operator: String,
    pub is_even: bool,
}

A Fredholm module (A, H, F) representing a K-homology class.

A Fredholm module consists of a -representation of A on H together with a bounded operator F = F with F² − 1 compact and [F, a] compact for all a ∈ A.

Fields

algebra: String

Name of the represented C*-algebra.

hilbert_space: String

Name of the Hilbert space.

operator: String

Name/description of the Fredholm operator F.

is_even: bool

Whether the module is even-graded (existence of a grading operator γ).

Implementations

impl FredholmModule

pub fn new( algebra: impl Into<String>, hilbert_space: impl Into<String>, operator: impl Into<String>, is_even: bool, ) -> Self

Construct a Fredholm module.

pub fn index(&self) -> i64

The Fredholm index of the module: index(P_+ F P_+) for the even case.

pub fn pairing_with_k_theory(&self, element: f64) -> f64

Pairing of the Fredholm module with a K-theory element (a projection p ∈ M_n(A)).

The pairing ⟨[F], [p]⟩ = index(p F p) is the analytic index.