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A heap is a set with a certain ternary operation that is self-distributive(TSD) and exemplified by a group with the operation $(x,y,z)\mapsto xy^{-1}z$.We introduce and investigate framed link invariants using heaps. In analogywith the knot group, we define the fundamental heap of framed links using grouppresentations. The fundamental heap is determined for some classes of linkssuch as certain families of torus and pretzel links. We show that for thesefamilies of links there exist epimorphisms from fundamental heaps to Vinbergand Coxeter groups, implying that corresponding groups are infinite. A relationto the Wirtinger presentation is also described. The cocycle invariant isdefined using ternary self-distributive (TSD) cohomology, by means of a statesum that uses ternary heap $2$-cocycles as weights. This invariant correspondsto a rack cocycle invariant for the rack constructed by doubling of a heap,while colorings can be regarded as heap morphisms from the fundamental heap.For the construction of the invariant, first computational methods for the heapcohomology are developed. It is shown that the cohomology splits into twotypes, called degenerate and nondegenerate, and that the degenerate part is onedimensional. Subcomplexes are constructed based on group cosets, that allowcomputations of the nondegenerate part. Computations of the cocycle invariantsare presented using the cocycles constructed, and conversely, it is proved thatthe invariant values can be used to derive algebraic properties of thecohomology.

Fundamental Heap for Framed Links and Ribbon Cocycle Invariants