Coarse Version Of Homotopy Theory
Axiomatic Structure
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The aim is to look at notions of cofibration category within the world of coarse geometry. Then use the cofibration category machinery to define coarse homotopy groups, and to compute these groups for coarse spheres. There is an abstract notion of a cell complex defined in the context of a cofibration category. In the coarse setting, such cell complexes will have a more geometric definition, and precisely a coarse CW-complex is a cell complex. The ultimate goal of such computations is a version of the Whitehead Theorem relating coarse homotopy groups and coarse homotopy equivalences for cell c...
The aim is to look at notions of cofibration category within the world of coarse geometry. Then use the cofibration category machinery to define coarse homotopy groups, and to compute these groups for coarse spheres. There is an abstract notion of a cell complex defined in the context of a cofibration category. In the coarse setting, such cell complexes will have a more geometric definition, and precisely a coarse CW-complex is a cell complex. The ultimate goal of such computations is a version of the Whitehead Theorem relating coarse homotopy groups and coarse homotopy equivalences for cell com- plexes. Abstract versions of the Whitehead Theorem are known for cofibration categories, so these abstract results can be related to something more geometric.
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