Abstract
The notion of a phantom category is a recently coined term, referring to a nontrivial triangulated or dg-category with vanishing Grothendieck group and/or Hochschild homology. In this note, we refer to categories with vanishing Grothendieck group as K-phantoms and categories with vanishing Hochschild homology and HH-phantoms. When both of these invariants vanish, we follow [13], and refer to these categories simply as phantoms.
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Acknowledgements
We would like to whole-heartedly thank C. Böhning, H. Graf von Bothmer, P. Sosna, D. Orlov, S. Galkin, A. Kuznetsov, D. Auroux, C. Vafa, E. Sharpe, and S. Gukov, for inspiring these ideas through many extremely useful discussions. The first and second authors were funded by FWF Grant P20778, and an ERC Grant (GEMIS). The third author was funded by NSF Grant DMS0600800, NSF FRG Grant DMS-0652633, FWF Grant P20778, and an ERC Grant (GEMIS).
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Favero, D., Haiden, F., Katzarkov, L. (2014). An Orbit Construction of Phantoms, Orlov Spectra, and Knörrer Periodicity. In: Castano-Bernard, R., Catanese, F., Kontsevich, M., Pantev, T., Soibelman, Y., Zharkov, I. (eds) Homological Mirror Symmetry and Tropical Geometry. Lecture Notes of the Unione Matematica Italiana, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-06514-4_2
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