Encomplexed Brown Invariant of Real Algebraic Surfaces in RP^3

Johan Björklund

doi:10.1007/s11512-012-0176-6

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arXiv · 1108.1566

Encomplexed Brown Invariant of Real Algebraic Surfaces in RP^3

Johan Björklund

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Abstract

We construct an invariant of parametrized generic real algebraic surfaces in RP^3 which generalizes the Brown invariant of immersed surfaces from smooth topology. The invariant is constructed using the self intersection, which is a real algebraic curve with points of three local characters: the intersection of two real sheets, the intersection of two complex conjugate sheets or a Whitney umbrella. The Brown invariant was expressed through a self linking number of the self intersection by Kirby and Melvin. We extend the definition of this self linking number to the case of parametrized generic real algebraic surfaces.

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BibTeX RIS

Johan Björklund. 2011-08-07. Encomplexed Brown Invariant of Real Algebraic Surfaces in RP^3. https://doi.org/10.1007/s11512-012-0176-6

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