Different bounds on the different Betti numbers of semi-algebraic sets

@inproceedings{Basu2001DifferentBO,
  title={Different bounds on the different Betti numbers of semi-algebraic sets},
  author={Saugata Basu},
  booktitle={Symposium on Computational Geometry},
  year={2001}
}
A classic result in real algebraic geometry due to Oleinik-Petrovsky, Thom and Milnor, bounds the {\em topological complexity} (the sum of the Betti numbers) of basic semi-algebraic sets. This bound is tight as one can construct examples having that many connected components. However, till now no significantly better bounds were known on the individual higher Betti numbers. In this paper we prove separate bounds on the different Betti numbers of basic semi-algebraic sets, as well as… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-2 of 2 references

A User’s Guide to Spectral Sequences, 2nd edn., Cambridge Studies in Advanced Mathematics

  • J. McCleary
  • 2001
Highly Influential
3 Excerpts

On the Betti numbers of real varieties

  • J. Milnor
  • Proc. Amer. Math. Soc.,
  • 1964
Highly Influential
4 Excerpts

Similar Papers

Loading similar papers…