Abstract.
We prove by combinatorial means new formulae for intersection numbers of twisted homology of hyperplane complements, thereby solving a conjecture of Aomoto.
Similar content being viewed by others
References
Aomoto, K.: Connection Problem for Difference Equations associated with Real Hyperplane Arrangements. Preprint (2000)
Aomoto, K., Kita, M.: Hypergeometric Functions (in Japanese), Springer Tokyo (1994)
Cho, K., Matsumoto, K.: Intersection theory for twisted cohomologies and twisted Riemann’s period relations, preprint
Kita, M., Yoshida, M.: Intersection theory for twisted cycles. Math.Nachr. 166, 287–304 (1994)
Kita, M., Yoshida, M.: Intersection theory for twisted cycles(II). Math.Nachr. 168, 171–190 (1994)
Kohno, T.: Homology of a local system on the complement of hyperplanes. Proc. Japan Acad. Ser. A. 62, 144–147 (1986)
Matsumoto, K.: Intersection numbers for logarithmic k-forms. Osaka J.Math. 35, 873–893 (1998)
Majima, H., Matsumoto, K., Takayama, N.: Quadratic relations for confluent hypergeometric functions. Preprint (2000)
Matsumoto, K., Sasaki, T., Takayama, N., Yoshida, M.: Monodromy of the hypergeometric differential equation of type (3,6) (I). Duke Math. J. 71, 403–426 (1993)
Orlik, P., Terao, H.: Arrangements of Hyperplanes, Springer Verlag, 1992
Orlik, P., Terao, H.: Arrangements and Hypergeometric Integrals. MSJ Memoirs 9, (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Togi, T. Intersection Numbers for Twisted Homology. manuscripta math. 114, 165–176 (2004). https://doi.org/10.1007/s00229-004-0454-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00229-004-0454-0