On the Haefliger-Hirsch-Wu invariants for embeddings and immersions |
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Authors: | A Skopenkov |
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Institution: | (1) Department of Differential Geometry, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia 119899, e-mail: skopenko@mccme.ru, RU |
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Abstract: | We prove beyond the metastable dimension the PL cases of the classical theorems due to Haefliger, Harris, Hirsch and Weber
on the deleted product criteria for embeddings and immersions. The isotopy and regular homotopy versions of the above theorems
are also improved. We show by examples that they cannot be improved further. These results have many interesting corollaries,
e.g.? 1) Any closed homologically 2-connected smooth 7-manifold smoothly embeds in .? 2) If and then the set of PL embeddings up to PL isotopy is in 1-1 correspondence with?.
Received: July 6, 2000 |
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Keywords: | , Embedding, deleted product, engulfing, singular set, metastable case, isotopy, immersion, smoothing, knotted tori, |
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