Encomplexed Brown invariant of real algebraic surfaces in ℝ$P$^{3}

Johan Björklund Department of Mathematics, Uppsala University


Arkiv for Matematik, 51, (2), 251-267, 2011.8
We construct an invariant of parametrized generic real algebraic surfaces in ℝ$P$^{3}which generalizes the Brown invariant of immersed surfaces from smooth topology. The invariant is constructed using self-intersections, which are real algebraic curves with points of three local characters: the intersection of two real sheets, the intersection of two complex conjugate sheets or a Whitney umbrella. In Kirby and Melvin (Local surgery formulas for quantum invariants and the Arf invariant, in$Proceedings of the Casson Fest$, Geom. Topol. Monogr.$7$, pp. 213–233, Geom. Topol. Publ., Coventry, 2004) the Brown invariant was expressed through a self-linking number of the self-intersection. We extend the definition of this self-linking number to the case of parametrized generic real algebraic surfaces.
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  title={Encomplexed Brown invariant of real algebraic surfaces in ℝ$P$^{3}},
  author={Johan Björklund},
  booktitle={Arkiv for Matematik},
Johan Björklund. Encomplexed Brown invariant of real algebraic surfaces in ℝ$P$^{3}. 2011. Vol. 51. In Arkiv for Matematik. pp.251-267. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203636003689048.
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