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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Semi-algebraic partition and basis of Borel-Moore homology of hyperplane arrangements


Authors: Ko-Ki Ito and Masahiko Yoshinaga
Journal: Proc. Amer. Math. Soc. 140 (2012), 2065-2074
MSC (2010): Primary 32S22; Secondary 14N20
Published electronically: October 18, 2011
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Abstract: We describe an explicit semi-algebraic partition for the complement of a real hyperplane arrangement such that each piece is contractible and so that the pieces form a basis of Borel-Moore homology. We also give an explicit correspondence between the de Rham cohomology and the Borel-Moore homology.


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Additional Information

Ko-Ki Ito
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
Email: koki@kurims.kyoto-u.ac.jp

Masahiko Yoshinaga
Affiliation: Department of Mathematics, Faculty of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
Email: mhyo@math.kyoto-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11168-7
PII: S 0002-9939(2011)11168-7
Received by editor(s): February 10, 2011
Published electronically: October 18, 2011
Additional Notes: The first author was supported in part by JSPS Grant-in-Aid for Challenging Exploratory Research No. 21654003.
The second author was supported in part by JSPS Grant-in-Aid for Young Scientists (B) No. 20740038.
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.