On the topological complexity of Grassmann manifolds
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Vimala Ramani
Abstract
We prove that the topological complexity of a quaternionic flag manifold is half of its real dimension. For the real oriented Grassmann manifolds G͠n,k, 3 ≤ k ≤ [n/2], the zero-divisor cup-length of the rational cohomology of G͠n,k is computed in terms of n and k which gives a lower bound for the topological complexity of G͠n,k, TC(G͠n,k). When k = 3, it is observed in certain cases that better lower bounds for TC(G͠n,3) are obtained using ℤ2-cohomology.
Dedicated to Professor Parameswaran Sankaran on the occasion of his 60th birthday
(Communicated by Július Korbaš)
Acknowledgement
The author would like to thank Professor Parameswaran Sankaran for the encouragement and the very useful discussions. The author also would like to thank Professor Aniceto Murillo for sending a copy of his paper [15].
The author is highly indebted to the referee for the valuable comments and suggestions, in particular for pointing out a lacuna in the proof of Theorem 1.5 in the case n = 7 in the previous version; the referee’s helpful suggestions have made the proof of Theorem 1.5 thorough and clear.
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© 2020 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Regular papers
- Monadic pseudo BE-algebras
- Quadruple construction of decomposable double MS-algebras
- Fibonacci numbers in generalized Pell sequences
- Solutions of a generalized markoff equation in Fibonacci numbers
- Root separation for polynomials with reducible derivative
- Quadratic refinements of Young type inequalities
- Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means
- Integration with respect to deficient topological measures on locally compact spaces
- Differential subordinations and Pythagorean means
- Analogs of Hayman’s Theorem and of logarithmic criterion for analytic vector-valued functions in the unit ball having bounded L-index in joint variables
- Unbounded oscillation of fourth order functional differential equations
- Oscillation criteria for a class of nonlinear discrete fractional order equations with damping term
- Entropy as an integral operator: Erratum and modification
- Unital topology on a unital l-group
- On the topological complexity of Grassmann manifolds
- Properties and methods of estimation for a bivariate exponentiated Fréchet distribution
- Existence and Hyers-Ulam stability results for a class of fractional order delay differential equations with non-instantaneous impulses
- Two semigroup rings associated to a finite set of meromorphic functions
