Corpus ID: 118050133

Regular embeddings of manifolds and topology of configuration spaces

@article{Karasev2010RegularEO,
  title={Regular embeddings of manifolds and topology of configuration spaces},
  author={R. Karasev},
  journal={arXiv: Algebraic Topology},
  year={2010}
}
  • R. Karasev
  • Published 2010
  • Mathematics
  • arXiv: Algebraic Topology
  • For a topological space $X$ we study continuous maps $f : X\to \mathbb R^m$ such that images of every pairwise distinct $k$ points are affinely (linearly) independent. Such maps are called affinely (linearly) $k$-regular embeddings. We investigate the cohomology obstructions to existence of regular embeddings and give some new lower bounds on the dimension $m$ as function of $X$ and $k$, for the cases $X$ is $\mathbb R^n$ or $X$ is an $n$-dimensional manifold. In the latter case, some nonzero… CONTINUE READING
    Regular Maps on Cartesian Products and Disjoint Unions of Manifolds
    On Highly Regular Embeddings
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    Equivariant Topology of Configuration Spaces
    20

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 18 REFERENCES
    Multiplicity of continuous maps between manifolds
    4
    Complements of Discriminants of Smooth Maps: Topology and Applications
    8
    $k$-regular embeddings of the plane
    26
    2-regular maps on smooth manifolds
    14
    k-Regular Mappings of 2 n -Dimensional Euclidean Space
    15
    Fixed point free involutions and equivariant maps
    115
    Cohomology of finite groups
    245
    ON THE REALIZATION OF COMPLEXES IN EUCLIDEAN SPACES II
    5