Using the Particle Model to Find Structure in Eilenberg-MacLane Spaces

We introduce two models, the bar construction and the particle model, for a collection of spaces known as Eilenberg-MacLane spaces. These spaces can be used as building blocks for other spaces and are of great interest throughout topology. We use these models to compute the homology groups for one Eilenberg-MacLane space in an intuitive and accessible way, and then show how the models can be used to determine the cell structure for additional cases using combinatorial arguments. An introduction to cellular homology and examples are included along the way

Invariants for the Smale space associated to an expanding endomorphism of a flat manifold

We study invariants associated to Smale spaces obtained from an expanding endomorphism on a (closed connected Riemannian) flat manifold. Specifically, the relevant invariants are the $K$-theory of the associated $C^*$-algebras and Putnam's homology theory for Smale spaces. The latter is isomorphic to the groupoid homology of the groupoids used to construct the $C^*$-algebras.Comment: 21 page

Using the Particle Model to Find Structure in Eilenberg-MacLane Spaces

We introduce two models, the bar construction and the particle model, for a collection of spaces known as Eilenberg-MacLane spaces. These spaces can be used as building blocks for other spaces and are of great interest throughout topology. We use these models to compute the homology groups for one Eilenberg-MacLane space in an intuitive and accessible way, and then show how the models can be used to determine the cell structure for additional cases using combinatorial arguments. An introduction to cellular homology and examples are included along the way