Geodesic
Real four-dimensional biquadrics
Izvestiya. Mathematics , Tome 75 (2011) no. 2, pp. 371-394

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We consider intersections of two real five-dimensional quadrics, which are referred to for brevity as real four-dimensional biquadrics. Their rigid isotopy classes were described long ago: there are 16 such classes. We prove that the rigid isotopy class of a non-singular real four-dimensional biquadric is uniquely determined by the topological type of its real part. To do this, we calculate the dimensions of the cohomology spaces of the real part of a four-dimensional biquadric.
Keywords: rigid isotopy classes, coarse isotopy classes, index function.
Mots-clés : biquadrics 
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     author = {V. A. Krasnov},
     title = {Real four-dimensional biquadrics},
     journal = {Izvestiya. Mathematics },
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     year = {2011},
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     url = {http://geodesic.mathdoc.fr/item/IM2_2011_75_2_a5/}
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V. A. Krasnov. Real four-dimensional biquadrics. Izvestiya. Mathematics , Tome 75 (2011) no. 2, pp. 371-394. http://geodesic.mathdoc.fr/item/IM2_2011_75_2_a5/