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| Buchstaber Invariants of Universal Complexes |
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Citation： |
Yi SUN.Buchstaber Invariants of Universal Complexes[J].Chinese Annals of Mathematics B,2017,38(6):1335~1344 |
| Page view： 1184
Net amount： 1520 |
Authors： |
Yi SUN; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11371093, 10931005). |
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| 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. |
Keywords： |
Buchstaber invariant, Universal complex, Lifting problem |
Classification： |
57S25, 52B05, 05E45 |
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