7 papers
A distance between maps via interleavings of relative Sullivan algebras
Katsuhiko Kuribayashi, Takahito Naito, Kengo Sekizuka +2
In this article, we consider extended tame persistence commutative differential graded algebras (CDGAs) associated with relative Sullivan algebras. In particular, if the relative S…
The equalities of interleaving distances and cohomology interleavings of spaces over
Katsuhiko Kuribayashi, Takahito Naito, Shun Wakatsuki +1
The cohomology interleaving distance (CohID) is defined and considered in the category of persistent differential graded modules over a field. As a consequence, we show that, in th…
Minimal projective resolution and magnitude homology of geodetic metric spaces
Yasuhiko Asao, Shun Wakatsuki
Asao-Ivanov showed that magnitude homology is a Tor functor, hence we can compute it by giving a projective resolution of a certain module. In this article, we compute magnitude ho…
Dominance complexes, neighborhood complexes and combinatorial Alexander duals
Takahiro Matsushita, Shun Wakatsuki
We show that the dominance complex of a graph coincides with the combinatorial Alexander dual of the neighborhood complex of the co…
Independence complexes of -grid graphs
Takahiro Matsushita, Shun Wakatsuki
We determine the homotopy types of the independence complexes of the -square grid graphs. In fact, we show that these complexes are homotopy equivalent to wedges of s…
Cartan calculi on the free loop spaces
Katsuhiko Kuribayashi, Takahito Naito, Shun Wakatsuki +1
A typical example of a Cartan calculus consists of the Lie derivative and the contraction with vector fields of a manifold on the derivation ring of the de Rham complex. In this ma…
Independence complexes of and -grid graphs
Takahiro Matsushita, Shun Wakatsuki
We determine the homotopy types of the independence complexes of and -square grid graphs. In fact, they are homotopy equivalent to wedges of spheres.