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Topological Shift Spaces
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Dieter Betten
Published/Copyright:
July 27, 2005
Abstract
Two of the problems listed in [14, 74.17] ask to prove or disprove the following statements:
For each differentiable planar map ƒ : IR2 → IR2 the set of all differentials defines a spread of IR4.
If the differentials of a differentiable map ƒ : IR2 → IR2 define a spread of IR4 then the map ƒ is planar.
By restricting to vertical 3-dimensional subspaces, we get the notion of a 3-dimensional shift space, and for differentiable shift spaces we may formulate analogous problems A′ and B′. Under the additional assumption that there exists a 1-dimensional group of shears, we prove A′ and B′ for 3-dimensional shift spaces and—as a corollary—also A and B for 4-dimensional shift planes.
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Published Online: 2005-07-27
Published in Print: 2005-01-01
© de Gruyter
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- Three-Dimensional Projection Bodies
- Witt-Type Theorems for Grassmannians and Lie Incidence Geometries
- Existence of Vector Bundles of Rank Two with Sections
- On the Quantum Cohomology of Some Fano Threefolds
- Eigenspaces of Linear Collineations
- Residues for Holomorphic Foliations of Singular Pairs
- On the Length of the Cut Locus for Finitely Many Points
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- The Thick Frame of a Weak Twin Building
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Articles in the same Issue
- Three-Dimensional Projection Bodies
- Witt-Type Theorems for Grassmannians and Lie Incidence Geometries
- Existence of Vector Bundles of Rank Two with Sections
- On the Quantum Cohomology of Some Fano Threefolds
- Eigenspaces of Linear Collineations
- Residues for Holomorphic Foliations of Singular Pairs
- On the Length of the Cut Locus for Finitely Many Points
- Topological Shift Spaces
- The Thick Frame of a Weak Twin Building
- Free Planes in Lattice Sphere Packings
- Euler Integration and Euler Multiplication
