Module simplicial 

Finite covers, nerves, global geodesics, and fundamental groups.

A Bounded chart domain and BuildNodes implementation produce the nodes consumed by NerveComplex. Their overlaps determine a NerveTopology, whose fundamental group is exposed as a GroupPresentation; the same finite structure drives certified global geodesic search through Geodesic and GeodesicCertificate.

Structs

Abelianisation

The abelianisation G^ab = G/[G,G] of a finitely presented group, together with diagonal coordinates for the images of its original generators.

ArcPoly

A polyline with its cumulative arc length, so sampling is O(log n).

Basin

A distinct valley of the length functional: one geodesic from p to q that is a strict local minimum of length among nearby paths.

Geodesic

The result of a global geodesic search over a NerveComplex.

GeodesicCertificate

Evidence describing whether a returned Geodesic is globally minimal.

NerveTopology

Everything the nerve’s 1- and 2-skeleta determine, computed once per type.

StaticGroupPresentation

A stack-backed GroupPresentation generated by group_presentation!.

StaticWord

A single relation, borrowed as a sub-slice of some StaticGroupPresentation’s single flat backing array.

Enums

StraighteningResult

Outcome of the local straightening phase used by NerveComplex::geodesic_path.

Traits

Bounded

Restricts the domain of Chart::to_local to some subset defined by a signed distance function in the tangent space at each point on a TangentBundle.

BuildNodes

The one-time recipe for producing a fixed node set Vec<B>.

GroupPresentation

A presentation of a group by generators and relations.

NerveComplex

A finite collection of TangentBundle charts whose injectivity domains together cover a manifold P, forming the nerve of the cover as a simplicial complex.

NerveComplexParameters

Numerical and combinatorial parameters for a finite NerveComplex.

Nodes

Sealed accessor for a memoized, canonical node set.