Annals of Combinatorics 4 (2000) 171-182


Lagrangian Matroids and Cohomology

Richard F. Booth1, Alexandre V. Borovik1, Israel M. Gelfand2, and David A. Stone3

1Department of Mathematics, UMIST, PO Box 88, Manchester M60 1QD, UK
  {alexandre.borovik, richard.booth}@umist.ac.uk

2Department of Mathematics,Rutgers University, New Brunswick,NJ 08903, USA
  igelfand@math.rutgers.edu

3Department of Mathematics, Brooklyn College, 2900 Bedford Avenue, Brooklyn, NY 11210-2889, USA

Received March 15, 1999

AMS Subject Classification: 05B35

Abstract. We prove that $\Delta$-matroids associated with maps on compact closed surfaces are representable, with the space of representation provided by cohomology of the surface with punctured points.

Keywords$\Delta$-matroid, Lagrangian symplectic matroid, cohomology, $CW$-complex


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