Mathematical Sciences: Topological Embeddings in Piecewise Linear Manifolds

维尼马将继续他的研究几何拓扑。 要研究的问题涉及拓扑嵌入 分段线性流形和胞状映射 你好 除其他外，他将研究 分片线性4-流形中的邻域， 试图确定同伦等价的，局部简单的， 通过局部单连通， 空间. 理解4-结构的重要性 维流形在理论上越来越多地被认识到 物理学 甚至更高维的流形也起着重要的作用， 在当前流行的所谓“弦理论”中扮演的角色。

Venema will continue his research in geometric topology. The problems to be investigated involve topological embeddings into piecewise linear manifolds and cell-like mappings of compacta. Among other things he will investigate the structure of neighborhoods of compacta in piecewise linear 4-manifolds and try to determine whether homotopy-equivalent, locally simply- connected compacta are CE equivalent via locally simply-connected spaces. The importance of understanding the structure of 4- dimensional manifolds is increasingly recognized in theoretical physics. Even higher dimensional manifolds play an essential role in the so-called "string theory" of current vogue.