publication . Article . 1999

Transversality in generalized manifolds

Bryant, J.L.;
Open Access
  • Published: 01 Jun 1999 Journal: Topology and its Applications, volume 94, pages 7-12 (issn: 0166-8641, Copyright policy)
  • Publisher: Elsevier BV
Abstract
Abstract Suppose that X is a generalized n -manifold, n≥5 , satisfying the disjoint disks property, and M and Q are topological m - and q -manifolds, respectively, 1-LCC embedded in X , with n−m≥3 and n−q≥3 . We define what it means for M to be stably transverse to Q in X . In the metastable range, 3m≤2(n−1) and 3(m+q) , we show that there is an arbitrarily small homotopy of M to a 1-LCC embedding that is stably transverse to Q .
Subjects
free text keywords: Geometry and Topology, Combinatorics, Mathematics, Mathematical analysis, Transverse plane, Embedding, Manifold, Disjoint sets, Homotopy, Transversality, Topology, Generalized manifolds, Embeddings
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