An Introduction To The ∞-Category Of Motivic Coarse Spaces. A Series Of Talks

We introduce the category $\mathsf{BornCoarse}$ of bornological coarse spaces, define the category of motivic coarse spaces $\mathrm{Spc}\, \chi$, consider some examples of coarse homology theories, including coarse ordinary homology, equivariant ordinary homology and equivariant coarse topological $K$-theory. We discuss also connections with index theory. This series of talks is based on the book by Ulrich Bunke and Alexander Engel “Homotopy Theory with Bornological Coarse Spaces”. Read more

1. Elements of unstable motivic homotopy theory, April 24, 2023
2. The category BornCoarse Of Bornological Coarse Spaces, May 8, 2023
3. (Co-)products, coarse equivalences and flasque spaces, May 12, 2023
4. Motivic Coarse Spectra $\mathrm{Sp}\, \chi\subset \mathrm{PSh}(\mathsf{BornCoarse})$, May 15, 2023
5. Examples Of Coarse Homology Theory, May 22, 2023

The page of the seminar (video links are also available there)

References

1. U. Bunke, “Coarse geometry,” arXiv (https://arxiv.org/abs/2305.09203)
2. Bunke, Ulrich & Engel, Alexander. (2016). Homotopy Theory with Bornological Coarse Spaces. 10.1007/978-3-030-51335-1