This paper proves a map from flow-spines to contact structures is surjective.
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5 results for “flow-spines”
problem Mapping flow-spines to contact structures in 3-manifolds.
method Using positive flow-spines and contact structures, proving surjectivity.
result The map from flow-spines to contact structures is surjective.
A flow-spine of a 3-manifold is a spine admitting a flow that is transverse to the spine, where the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. We say that a contact structure on a closed, connected, oriented 3-manifold is supported by a flow-spine if it has a contact form w…
Paper proves S-stability of foliations on flow-spines with transverse Reeb flow.
problem Characterizing S-stable foliations on flow-spines with transverse Reeb flow.
method Introduced S-stability for foliations on branched simple polyhedrons and proved stability for 1-forms with .
result Proved the number of simple tangency points of an S-stable foliation on a flow-spine is at least 2.
The abstract extends Reidemeister theorem to 3-manifolds using diagrams of links and bands.
problem Extending Reidemeister theorem to 3-manifolds.
method Defines diagrams for links and bands on spines and flow-spines of 3-manifolds and describes combinatorial moves.
result Reproves and extends Brand et al. result on 3-manifolds.
Properly immersed curves in arbitrary surfaces via apparent contours on spines of traversing flowsmath.GT
The paper studies curves in surfaces using flow-spines and apparent contours.
problem Understanding curves in arbitrary surfaces using flow-spines and apparent contours.
method By considering generic curves and their apparent contours relative to a traversing flow, the paper reconstructs curves and allows them to vary up to homotopy.
result A finite set of local moves on decorated graphs allows for the reconstruction and variation of curves within a fixed generic flow.