Buchstaber Invariants of Universal Complexes

作者：Sun, Yi^*

来源：Chinese Annals of Mathematics Series B, 2017, 38(6): 1335-1344.

DOI：10.1007/s11401-017-1041-5

• Buchstaber invariant
• universal complex
• Lifting problem

Davis and Januszkiewicr introdreed (real and complex) oniversal 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 in of K as the obstruction to fittings 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 liondegenerate map from 3 -dimensional real universal complex to 4 -dimensional complex universal complex.

• 出版日期2017-11
• 单位复旦大学