Geodesic
The Dimension Conjecture: Solution and Future Prospects
Matematičeskie zametki, Tome 112 (2022) no. 5, pp. 784-800

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Counterexamples to the dimension conjecture in CR geometry are constructed. This conjecture is organically related to the model surface method; it was refined as the method was developed. On the one hand, these counterexamples give a final negative solution of the conjecture in its original setting. On the other hand, they make it possible to distinguish a natural class of manifolds (nondegenerate manifolds) for which the conjecture makes sense and is of interest. The main questions arising in this direction are formulated. A series of examples interesting from the point of view of the model surface method are considered.
Keywords: CR manifold, Bloom–Graham type.
Mots-clés : automorphism 
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     author = {M. A. Stepanova},
     title = {The {Dimension} {Conjecture:} {Solution} and {Future} {Prospects}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {784--800},
     publisher = {mathdoc},
     volume = {112},
     number = {5},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_5_a10/}
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M. A. Stepanova. The Dimension Conjecture: Solution and Future Prospects. Matematičeskie zametki, Tome 112 (2022) no. 5, pp. 784-800. http://geodesic.mathdoc.fr/item/MZM_2022_112_5_a10/