Anosov theorem for coincidences on special solvmanifolds of type $(\mathrm {R})$
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- by Ku Yong Ha, Jong Bum Lee and Pieter Penninckx PDF
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Abstract:
Suppose that $S$ and $S’$ are simply connected solvable Lie groups of type $(\mathrm {R})$ with the same dimension. We show that the Lefschetz coincidence numbers of maps $f,g:\Gamma \backslash S\to \Gamma ’\backslash S’$ between special solvmanifolds $\Gamma \backslash S\to \Gamma ’\backslash S’$ can be computed algebraically as follows: \[ L(f,g) = \det (G_* - F_*), \] where $F_*,G_*$ are the matrices, with respect to any preferred bases, of morphisms of Lie algebras induced by $f$ and $g$. This generalizes a recent result by S. W. Kim and J. B. Lee to special solvmanifolds of type (R). Moreover, we can drop the dimension match condition imposed in the latter result.References
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Additional Information
- Ku Yong Ha
- Affiliation: Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
- Email: kyha@sogang.ac.kr
- Jong Bum Lee
- Affiliation: Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
- MR Author ID: 343537
- Email: jlee@sogang.ac.kr
- Pieter Penninckx
- Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Campus Kortrijk, B-8500 Kortrijk, Belgium
- Email: pieter.penninckx@kuleuven-kortrijk.be
- Received by editor(s): August 11, 2009
- Received by editor(s) in revised form: May 31, 2010
- Published electronically: November 5, 2010
- Additional Notes: The second-named author is supported partially by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MOST) (No. R01-2007-000-10097-0) and by the Sogang University Research Grant of 2010.
The third-named author is supported by a Ph.D. fellowship of the Research Foundation-Flanders (FWO) - Communicated by: Alexander N. Dranishnikov
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2239-2248
- MSC (2010): Primary 55M20, 54H25, 57S30
- DOI: https://doi.org/10.1090/S0002-9939-2010-10721-9
- MathSciNet review: 2775401