Struct CellularApproximation 

pub struct CellularApproximation {
    pub source: CwComplex,
    pub target: CwComplex,
}

Cellular approximation theorem and homotopy equivalence.

Provides combinatorial tools for cellular maps and homotopy equivalences between CW complexes.

Fields

source: CwComplex

Source complex.

target: CwComplex

Target complex.

Implementations

impl CellularApproximation

pub fn new(source: CwComplex, target: CwComplex) -> Self

Create a cellular approximation instance.

pub fn is_cellular_by_dim(&self) -> bool

Check if a map between k-skeleta is cellular: a map f: X → Y is cellular if f(X^k) ⊂ Y^k for all k. Checked by comparing max dimensions.

pub fn homotopy_equivalent_homology(&self) -> bool

Homotopy equivalence check: two complexes are homotopy equivalent if they have the same Betti numbers and torsion coefficients.

pub fn map_degree(&self) -> i32

Degree of a map between spheres (from induced map on top homology). Returns the sum of boundary signs (simplified computation).

pub fn whitehead_equivalent(&self) -> bool

Whitehead theorem: for CW complexes, a map inducing isomorphisms on all homotopy groups is a homotopy equivalence. Here approximated by homology.

Trait Implementations

impl Clone for CellularApproximation

fn clone(&self) -> CellularApproximation

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for CellularApproximation

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.