Abstract
Davis and Januszkiewicz introduced (real and complex) universal complexes to give an equivalent definition of characteristic maps of simple polytopes, which now can be seen as “colorings”. The author derives an equivalent definition of Buchstaber invariants of a simplicial complex K, then interprets the difference of the real and complex Buchstaber invariants of K as the obstruction to liftings of nondegenerate simplicial maps from K to the real universal complex or the complex universal complex. It was proved by Ayzenberg that real universal complexes can not be nondegenerately mapped into complex universal complexes when dimension is 3. This paper presents that there is a nondegenerate map from 3-dimensional real universal complex to 4-dimensional complex universal complex.
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Acknowledgments
The authors would like to thank the editors and the anonymous referees for their valuable comments and helpful suggestions that helped to improve the quality of the paper. Moreover, the author would like to thank his supervisor Prof. Kefeng Liu for his constant encouragement and help.
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This work was supported by the National Natural Science Foundation of China (Nos. 11371093, 10931005).
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Sun, Y. Buchstaber invariants of universal complexes. Chin. Ann. Math. Ser. B 38, 1335–1344 (2017). https://doi.org/10.1007/s11401-017-1041-5
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DOI: https://doi.org/10.1007/s11401-017-1041-5