Secondary cup and cap products in coarse geometry

Coarse Geometry and Randomness

1 Introductory graph and metric notions 5 1.1 The Cheeger constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Expander graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Isoperimetric dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Rough isome...

Cup Products in Computational Topology

Topological persistence methods provide a robust framework for analyzing large point cloud datasets topologically, and have been applied with great success towards homology computations on simplicial complexes. In this paper, we apply the persistence algorithm towards calculating a set of invariants related to the cup product structure on the cohomology ring for a space. These invariants expres...

Note on Cup-products

Coarse geometry and asymptotic dimension

We prove that two spaces, whose coarse structures are induced by metrisable compactifications, are coarsely equivalent if and only if their (Higson) coronas are homeomorphic. We introduce translation C∗-algebras for coarse spaces which admit a countable, uniformly bounded cover using projection-valued measures. This was already done in [Roe03]. Here we give a more complete exposition on the sub...

Coarse Geometry and K-homology