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Mário J. Edmundo; Luca Prelli
Invariance of $o$-minimal cohomology with definably compact supports
Confluentes Mathematici, 7 no. 1 (2015), p. 35-53, doi: 10.5802/cml.17
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Class. Math.: 03C64, 55N30
Keywords: $o$-minimal structures, $o$-minimal cohomology.

Résumé - Abstract

In this paper we find general criteria for invariance and finiteness results for $o$-minimal cohomology in an arbitrary $o$-minimal structure. We apply our criteria and obtain new invariance and finiteness results for $o$-minimal cohomology in $o$-minimal expansions of ordered groups and for the $o$-minimal cohomology of definably compact definable groups in arbitrary $o$-minimal structures.

Bibliography

[1] A. Berarducci and A. Fornasiero O-minimal cohomology: finiteness and invariance results J. Math. Logic 9 (2) (2009) 167–182.  MR 2679438 |  Zbl 1236.03030
[2] A. Berarducci and M. Otero O-minimal fundamental group, homology and manifolds J. London Math. Soc. 65 (2) (2002) 257–270.  MR 1883182 |  Zbl 1013.03044
[3] J. Bochnak, M. Coste and M-F. Roy Real algebraic geometry Springer-Verlag 1998.  MR 1659509 |  Zbl 0633.14016
[4] G. Bredon Sheaf theory Second Edition Springer-Verlag 1997.  MR 1481706 |  Zbl 0874.55001
[5] M. Coste An introduction to $o$-minimal geometry Dip. Mat. Univ. Pisa, Dottorato di Ricerca in Matematica, Istituti Editoriali e Poligrafici Internazionali, Pisa (2000).
[6] M. Carral and M. Coste Normal spectral spaces and their dimensions J. Pure and Appl. Algebra 30 (3) (1983) 227–235.  MR 724034 |  Zbl 0525.14015
[7] M. Coste and M.-F. Roy La topologie du spectre réel in Ordered fields and real algebraic geometry, Contemporary Mathematics 8 (1982) 27–59.  MR 653174 |  Zbl 0485.14007
[8] H. Delfs Homology of locally semialgebraic spaces LNM 1484 Springer-Verlag 1991.  MR 1176311 |  Zbl 0751.14033
[9] L. van den Dries Tame topology and $o$-minimal structures Cambridge University Press 1998.  MR 1633348 |  Zbl 0953.03045
[10] M. Edmundo, G. Jones and N. Peatfield Sheaf cohomology in $o$-minimal structures J. Math. Logic 6 (2) (2006) 163–179.  MR 2317425 |  Zbl 1120.03024
[11] M. Edmundo, M. Mamino and L. Prelli On definably proper maps Fund. Math. (to appear).
[12] M. Edmundo and M. Otero Definably compact abelian groups J. Math. Logic 4 (2) (2004) 163–180.  MR 2114966 |  Zbl 1070.03025
[13] M. Edmundo and L. Prelli Poincaré - Verdier duality in $o$-minimal structures Ann. Inst. Fourier Grenoble 60 (4) (2010) 1259–1288. Cedram |  MR 2722241 |  Zbl 1235.03070
[14] M. Edmundo and L. Prelli Sheaves on T-topologies J. Math. Soc. Japan (to appear).
[15] M. Edmundo and G. Terzo A note on generic subsets of definable groups Fund. Math. 215 (1) (2011) 53–65.  MR 2851701 |  Zbl 1244.03115
[16] M. Edmundo and A. Woerheide Comparision theorems for $o$-minimal singular (co)homology Trans. Amer. Math. Soc. 360 (9) (2008) 4889–4912.  MR 2403708 |  Zbl 1153.03010
[17] P. Eleftheriou A semi-linear group which is not affine Ann. Pure Appl. Logic 156 (2008) 287 – 289.  MR 2484486 |  Zbl 1155.03020
[18] P. Eleftheriou, Y. Peterzil and J. Ramakrishnan Interpretable groups are definable J. Math. Log. 14 1450002 (2014) [47 pages].  MR 3225588
[19] A. Fornasiero O-minimal spectrum Unpublished, 33pp, 2006. http://www.dm.unipi.it/~fornasiero/articles/spectrum.pdf
[20] R. Godement Théorie des faisceaux Hermann 1958.  MR 102797
[21] B. Iversen Cohomology of sheaves Springer Verlag 1986.  MR 842190 |  Zbl 1272.55001
[22] M. Kashiwara and P. Schapira Sheaves on manifolds Springer Verlag 1990.  MR 1074006 |  Zbl 0709.18001
[23] M. Otero A survey on groups definable in $o$-minimal structures in Model Theory with Applications to Algebra and Analysis, vol. 2, Editors: Z. Chatzidakis, D. Macpherson, A. Pillay and A. Wilkie, LMS LNS 350 Cambridge Univ. Press (2008) 177–206  MR 2436142 |  Zbl 1166.03016
[24] Y. Peterzil and C. Steinhorn Definable compactness and definable subgroups of $o$-minimal groups J. London Math. Soc. 59 (2) (1999) 769–786.  MR 1709079 |  Zbl 0935.03047
[25] A. Pillay On groups and fields definable in $o$-minimal structures J. Pure Appl. Algebra 53 (1988) 239 – 255.  MR 961362 |  Zbl 0662.03025
[26] A. Pillay Sheaves of continuous definable functions J. Symb. Logic 53 (4) (1988) 1165–1169.  MR 973106 |  Zbl 0683.03018
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