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Virtual Betti numbers of real algebraic varieties

✍ Scribed by Clint McCrory; Adam Parusiński

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
105 KB
Volume
336
Category
Article
ISSN
1631-073X

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✦ Synopsis

We show that for all i 0 the i-th mod 2 Betti number of compact nonsingular real algebraic varieties has a unique extension to a virtual Betti number β i defined for all real algebraic varieties, such that if Y is a closed subvariety of X then β i (X) = β i (X \ Y ) + β i (Y ). We show by example that there is no natural weight filtration on the Z 2 -cohomology of real algebraic varieties with compact supports such that the virtual Betti numbers are the weighted Euler characteristics.

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