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The topology of polynomial varieties. (English) Zbl 0970.14009
Cossey, John (ed.) et al., Geometric group theory down under. Proceedings of a special year in geometric group theory, Canberra, Australia, July 14-19, 1996. Berlin: de Gruyter. 1-8 (1999).
Summary: We show that the affine Cremona group \({\mathcal C} (n)\) has the homotopy type of the general linear group \(GL_n(\mathbb{C})\) and that two closed related spaces, the group of elementary transformations and the space of polynomial transformations with non-zero jacobian, have the same homotopy type; we introduce the polynomial varieties as spaces of polynomial solutions of algebraic equations and show that they have the homotopy type of a finite CW-complex.
For the entire collection see [Zbl 0910.00040].
14E07 Birational automorphisms, Cremona group and generalizations
14F35 Homotopy theory and fundamental groups in algebraic geometry
14J50 Automorphisms of surfaces and higher-dimensional varieties
20G15 Linear algebraic groups over arbitrary fields