Mathematical Sciences: Topological Embeddings in Piecewise Linear Manifolds

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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.