论文标题
在拓扑卡莱 - 夏兰群岛上的猜想
On the topological Kalai-Meshulam conjecture
论文作者
论文摘要
Chudnovsky，Scott，Seymour和Spirkl最近证明了Kalai和Meshulam的猜想，表明图形的独立性复合物的减少了，而没有诱导长度的诱导循环的三个以三分为{-1,0,1,1}。 Gauthier早些时候证明，假设是否没有诱发这些长度的循环。 Kalai和Meshulam还指出了更强的拓扑猜想，总贝蒂数在{0,1}中。在此方面，我们证明了与Gauthier相同的环境中更强有力的陈述：独立络合物是可缩度或同等于球体的同性恋。我们猜想它也存在于一般环境中。
Chudnovsky, Scott, Seymour and Spirkl recently proved a conjecture by Kalai and Meshulam stating that the reduced Euler characteristic of the independence complex of a graph without induced cycles of length divisible by three is in {-1,0,1}. Gauthier had earlier proved that assuming no cycles of those lengths, induced or not. Kalai and Meshulam also stated a stronger topological conjecture, that the total betti numbers are in {0,1}. Towards that we prove an even stronger statement in the same setting as Gauthier: The independence complexes are either contractible or homotopy equivalent to spheres. We conjecture that it also holds in the general setting.
