论文标题
$ SO（3）$ - 不变$ g_2 $ -cobordisms
$SO(3)$-invariant $G_2$-cobordisms
论文作者
论文摘要
我们研究了6个manifold上稳定3形式的边界关系，这是封闭的$ sl（3; \ mathbb {c}）$ - 在6个manifold上通过封闭的$ G_2 $结构上的二进制关系。在$ so（3）$ - 对称性和共同点条件下，该关系降低到3个manifold上几何结构的关系。在这些情况下，我们证明了界限的关系是无反射性的，并且这种关系会引起更加僵化的关系。
We study a bordism relation for stable 3-forms on a 6-manifold, which is a binary relation on the set of closed $SL(3;\mathbb{C})$-structures on a 6-manifold via closed $G_2$-structures. Under $SO(3)$-symmetry and a co-associative condition the relation is reduced to a relation for geometric structures on a 3-manifold. Under these conditions we prove that the bordism relation is irreflexive and that the relation induces a more rigid one.
