Abstract
In this chapter we show that any compact real algebraic set is homeomorphic to the realization of a (real algebraic) resolution tower of type REFUN. This homeomorphism is an isomorphism of stratified sets for some algebraic stratification of the algebraic set. In combination with the results in Chapter V it brings us much closer to classifying real algebraic sets in all dimensions since we showed there that any resolution tower of type REFS is isomorphic to an algebraic resolution tower. Thus the only obstruction to our classifying all real algebraic sets is the difference between type UN and type S. We presume that there is an as yet unproven resolution of singularities theorem for rational functions which bridges this difference. In Section 4 of Chapter VII we prove this in low dimensions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Akbulut, S., King, H. (1992). Resolution Tower Structures on Algebraic Sets. In: Topology of Real Algebraic Sets. Mathematical Sciences Research Institute Publications, vol 25. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9739-7_6
Download citation
DOI: https://doi.org/10.1007/978-1-4613-9739-7_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-9741-0
Online ISBN: 978-1-4613-9739-7
eBook Packages: Springer Book Archive