The homotopy type of the matroid grassmannian

Biss, Daniel K.

doi:10.4007/annals.2003.158.929

Cited by 13 publications

(11 citation statements)

References 17 publications

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“…Some years later, the paper [Bis03] put forward a proof that the matroid Grassmannian MacP(k, n) is homotopy equivalent to the real Grassmannian Gr(k, n). Unfortunately, a serious mistake was found in the proof [Bis09], and the topology of MacP(k, n) remains poorly understood.…”

Section: The Positive Matroid Grassmannian Is Homeomorphic To a Ballmentioning

confidence: 99%

Positively oriented matroids are realizable

Ardila¹,

Rincón²,

Williams³

2017

J. Eur. Math. Soc.

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Section: The Positive Matroid Grassmannian Is Homeomorphic To a Ballmentioning

confidence: 99%

Positively oriented matroids are realizable

Ardila¹,

Rincón²,

Williams³

2017

J. Eur. Math. Soc.

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“…A connection between matroids [7,8] and string can be achieved via the Schild type action. In fact, Nieto [9,10] has observed that the Nambu-Goto action in the context of Schild formulation can be illustrated as a straightforward extension of the chirotype motion of oriented matroids.…”

Section: Introductionmentioning

confidence: 99%

A LINK BETWEEN p-BRANES, NAMBU–POISSON STRUCTURE AND MATROIDS

Guha

2004

Int. J. Geom. Methods Mod. Phys.

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Dedicated to the great mathematical physicist Professor Albert Schwarz on the occasion of his 70th birthday.Recently Nieto has proposed a link between oriented matroid theory and the Schild type action of p-branes. This particular matroid theory satisfies the local condition, i.e., the degenerate form must be closed. This allows us to explain the dynamics of p-branes in terms of Nambu-Poisson structure. In this paper using an infinitesimal canonical transformation of Nambu brackets we show that the helicity is conserved in the dynamics of p-branes. Applying Filippov algebra (or quantum Nambu bracket) we define a generalized Yang-Mills action in 4k space. We show that this action is equivalent to Dolan-Tchrakian type action.

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“…An important achievement in this context is the recent result of Biss [15] proving this conjecture whenever M is a "free oriented matroid". In this case the OMGrassmannian is the space of all oriented matroids of a given cardinality and rank, usually called the MacPhersonian.…”

Section: The Generalized Baues Conjecture For the Zonotopal Tilings Omentioning

confidence: 99%

“…15 The smallest possible example, with eight points, is described in [7], based on Example 1.4. Actually, for every n there are triangulations with essentially n 2 vertices and only O(n) flips [63].…”

Section: Dimension 3 Things Start To Get Complicatedmentioning

confidence: 99%

Geometric bistellar ﬂips: the setting, the context and a construction

Santos¹

2007

Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006

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Abstract.We give a self-contained introduction to the theory of secondary polytopes and geometric bistellar flips in triangulations of polytopes and point sets, as well as a review of some of the known results and connections to algebraic geometry, topological combinatorics, and other areas.As a new result, we announce the construction of a point set in general position with a disconnected space of triangulations. This shows, for the first time, that the poset of strict polyhedral subdivisions of a point set is not always connected. Mathematics Subject Classification (2000). Primary 52B11; Secondary 52B20.

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The homotopy type of the matroid grassmannian

Cited by 13 publications

References 17 publications

Positively oriented matroids are realizable

Positively oriented matroids are realizable

A LINK BETWEEN p-BRANES, NAMBU–POISSON STRUCTURE AND MATROIDS

Geometric bistellar ﬂips: the setting, the context and a construction

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