On The betti numbers of oriented Grassmannians and independent semi-invariants of binary forms
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Július Korbaš
Abstract
We present a complete functional formula expressing the ith ℤ2-Betti number of the oriented Grassmann manifold of oriented 3-dimensional vector subspaces in Euclidean n-space for i from the range determined by the characteristic rank of the canonical oriented 3-dimensional vector bundle over this manifold. The same formula explicitly exhibits the number of linearly independent semi-invariants of degree 3 of a binary form of degree n − 3. Using the approach and data presented in this note, analogous results can be obtained for the oriented Grassmann manifold of oriented 4-dimensional vector subspaces in Euclidean n-space and semi-invariants of degree 4 of a binary form of degree n − 4.
The author was supported in part by two grants of VEGA (Slovakia). He was also partially affiliated with the Mathematical Institute, Slovak Academy of Sciences, Bratislava.
Acknowledgement
The author thanks Peter Zvengrowski for comments on a version of this paper.
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© 2017 Mathematical Institute Slovak Academy of Sciences
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- Cyclic and rotational latin hybrid triple systems
- Notes on mildly distributive semilattices
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- On the upper and lower exponential density functions
- Quadratic permutations, complete mappings and mutually orthogonal latin squares
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- S-essential spectra and measure of noncompactness
- Unified approach to graphs and metric spaces
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