arXiv 1111.02492011-11math.AT

On realizing homology classes by maps of restricted complexity

Mark Grant, Andras Szucs

备注：: 13 pages; Final version, to appear in Bull. Lond. Math. Soc
DOI：: 10.1112/blms/bds090

英文摘要：

We show that in every codimension greater than one there exists a mod 2 homology class in some closed manifold (of sufficiently high dimension) which cannot be realized by an immersion of closed manifolds. The proof gives explicit obstructions (in terms of cohomology operations) for realizability of mod 2 homology classes by immersions. We also prove the corresponding result in which the word `immersion' is replaced by `map with some restricted set of multi-singularities'.

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