# Multiplicity of continuous maps between manifolds

@inproceedings{Karasev2010MultiplicityOC, title={Multiplicity of continuous maps between manifolds}, author={Roman N. Karasev}, year={2010} }

We consider a continuous map $f :M\to N$ between two manifolds and try to estimate its multiplicity from below, i.e. find a $q$-tuple of pairwise distinct points $x_1,..., x_q\in M$ such that $f(x_1) = f(x_2) = ... = f(x_q)$.
We show that there are certain characteristic classes of vector bundle $f^*TN-TM$ that guarantee a bound on the multiplicity of $f$. In particular, we prove some non-trivial bound on the multiplicity for a continuous map of a real projective space of certain dimension… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 19 REFERENCES

## Fixed point free involutions and equivariant maps

VIEW 2 EXCERPTS

## The genus and the category of configuration spaces

VIEW 2 EXCERPTS

## Braid group cohomologies and algorithm complexity

VIEW 2 EXCERPTS