Sum of embedded submanifolds

Csaba Nagy

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arXiv · 1705.03836

Sum of embedded submanifolds

Csaba Nagy

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Abstract

In an $n$-manifold $X$ each element of $H_{n-1}(X; \mathbb{Z}_2)$ can be represented by an embedded codimension-1 submanifold. Hence for any two such submanifolds there is a third one that represents the sum of their homology classes. We construct such a representative explicitly. We describe the analogous construction for codimension-2 co-oriented submanifolds, and examine the special case of oriented and/or co-oriented submanifolds. We also give a lower bound for the number of connected components of the intersection of two oriented codimension-1 submanifolds in terms of the homology classes they represent.

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Csaba Nagy. 2017-05-10. Sum of embedded submanifolds. https://arxiv.org/abs/1705.03836

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