Arkiv för Matematik

  • Ark. Mat.
  • Volume 51, Number 2 (2013), 251-267.

Encomplexed Brown invariant of real algebraic surfaces in ℝP3

Johan Björklund

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Abstract

We construct an invariant of parametrized generic real algebraic surfaces in ℝP3 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.

Article information

Source
Ark. Mat., Volume 51, Number 2 (2013), 251-267.

Dates
Received: 22 August 2011
Revised: 21 September 2012
First available in Project Euclid: 1 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907221

Digital Object Identifier
doi:10.1007/s11512-012-0176-6

Mathematical Reviews number (MathSciNet)
MR3090196

Zentralblatt MATH identifier
1370.14051

Rights
2012 © Institut Mittag-Leffler

Citation

Björklund, Johan. Encomplexed Brown invariant of real algebraic surfaces in ℝ P 3. Ark. Mat. 51 (2013), no. 2, 251--267. doi:10.1007/s11512-012-0176-6. https://projecteuclid.org/euclid.afm/1485907221


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References

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