arXiv subjects

Liman Chen

Publications and source records attributed to Liman Chen.

3 recordsLinked to original sources

arXiv2016

The topology of the moment-angle manifolds--On a conjecture of S. Gitler ans S. Lopez

Let $P$ be a simple polytope of dimension $n$ with $m$ facets and $P_{v}$ be a polytope obtained from $P$ by cutting off one vertex $v$. Let $Z=Z(P)$ and $Z_{v}=Z(P_{v})$ be the corresponding moment-angle manifolds. In \cite{[GL]} S.Gitler and S.López conjectured that: $Z_{v}$ is diffeomorphic to $\partial[(Z-int(D^{n+m}))\times D^{2}]\sharp \mathop{\sharp} \limits_{j=1}^{m-n} \binom{m-n}{j} (S^{j+2}\times S^{m+n-j-1})$, and they have proved the conjecture in the case $m<3n$. In this paper we prove the conjecture in general case.

math.GT↗

arXiv2016

The cohomology of S(n,k) relavent to Morava stablizer algebra

In this paper we redefine an increasing filtration on the the Hopf algebra S(n,k), From which we get a spectral sequence called May spectral sequence. As an application we computed $H^{*,*}S(n,n)$ at prime 2, $H^{*,*}S(3,2)$ at prime 3 and $H^{*,*}S(4,2)$ at prime $p\geqslant 5$

math.AT↗

arXiv2014

Moment-angle manifolds and connected sums of sphere products

This paper investigates the moment-angle manifolds whose cohomology ring is isomorphic to that of a connected sum of sphere products. We first give a example of moment-angle manifolds corresponding to a 4 dimentional simplicial polytope. It has the property that its cohomology ring is isomorphic to that of a connected sum of sphere products with one produt of thress spheres. Finally, we give some general properties of this kind of moment-angle manifolds.

math.AT↗