Abstract
We use Gromov’s K-area to define homology groups for compact smooth manifolds. In fact, this theory collects obstructions to the enlargeability of the manifold and its nontrivial submanifolds. Moreover, using the K-area homology we can rephrase some classic results about positive scalar curvature. We also show that the functor of K-area homology determines the functor of singular homology on the category of compact smooth manifolds.
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Acknowledgments
The author would like to thank Sebastian Goette and Jan Schlüter for their support in questions of topology.
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M. Listing was supported by the German Science Foundation and in Part by SFB/TR 71.
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Listing, M. Homology of finite K-area. Math. Z. 275, 91–107 (2013). https://doi.org/10.1007/s00209-012-1124-7
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DOI: https://doi.org/10.1007/s00209-012-1124-7