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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
Posted:
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
Posted:
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 after
28 years from publication.
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