Papers by Július Korbaš
Let p : E → B be a Serre fibration with E compact, B a connected finite CW -complex, and fiber ei... more Let p : E → B be a Serre fibration with E compact, B a connected finite CW -complex, and fiber either the real Grassmann manifold O(n)/O(2) × O(n − 2) or the complex Grassmann manifold U(n)/U(2) × U(n− 2), where n ≥ 4. We prove that if n is odd, then the fiber is totally non-homologous to zero in E with respect to Z2.
This paper gives an explicit formula for the Z2-cup-length of the Stiefel manifolds Vn,r for all ... more This paper gives an explicit formula for the Z2-cup-length of the Stiefel manifolds Vn,r for all 1 ≤ r ≤ n − 1, and for the projective Stiefel manifolds Xn,r with n > 2r − 1. Some partial results for the latter case when n ≤ 2r−1 are given, as well as some relations between the two cases. We also show the consequence for the Lyusternik-Shnirel’man category. 2010 MSC: Primary 57R19; Secondary 55M30.
Rendiconti del Circolo Matematico di Palermo, 1999
ABSTRACT We give a complete list of real projective Stiefel manifolds which admit almost complex ... more ABSTRACT We give a complete list of real projective Stiefel manifolds which admit almost complex structures and show that many of them are in fact complex manifolds.
Bol. Soc. Mat. Mexicana (3), 2009
Results for the vector field problem on projective Stiefel manifolds X n,r ∼ = O(n)/(O(n − r) × Z... more Results for the vector field problem on projective Stiefel manifolds X n,r ∼ = O(n)/(O(n − r) × Z 2), 2 ≤ r < n, are derived here; X n,1 is (n − 1)-dimensional real projective space, for which these results are classical. In particular, span(X n,r) for r = 2, 3, 4, for suitable (infinitely many) values of n is calculated. If r = 2 and n is odd, then additional difficulties present themselves, and one approach to dealing with this case using the Browder-Dupont invariant is discussed. Furthermore, when n = 8m − 1, by using an explicit version of the Hurwitz-Radon multiplications, we improve the lower bound for span(X n,2) to span(S n). Two general results and some conjectures on the span of X n,r are also presented.
This paper presents some results, using the characteristic rank recently introduced by the second... more This paper presents some results, using the characteristic rank recently introduced by the second named author, on those smooth manifolds which can serve as total spaces of smooth fibre bundles with fibres totally non-homologous to zero with respect to Z2. As the main results, first, some upper and lower bounds for the characteristic rank of those total spaces which need not be null-cobordant are derived; then, bounds for the characteristic rank of null-cobordant total spaces are deduced. Examples are shown, where the upper and lower bounds coincide; thus these bounds cannot be improved in general. All examples of manifolds considered are homogeneous spaces.
Differential Geometry and Its Applications - Proceedings of the 10th International Conference on DGA2007, 2008
Bulletin of The Belgian Mathematical Society-simon Stevin - BULL BELG MATH SOC-SIMON STEV, 2000
Bulletin of The Belgian Mathematical Society-simon Stevin - BULL BELG MATH SOC-SIMON STEV, 2000
… of the Winter School" Geometry and …, 1996
... A° « ffs,,[(A+)2,(A+)2,A++,A+&quot;]/ c) for mixed parities, say k even and / odd, agai... more ... A° « ffs,,[(A+)2,(A+)2,A++,A+&quot;]/ c) for mixed parities, say k even and / odd, again A&quot;1 = 0, A&quot;0 is torsion free, and A&#x27;° «#,A+)2 ,A.,( ]/ d) in all cases H,ti is a subalgebra of A&#x27;(Gn,*) = K°(Gtk)- Page 13. 9 6 J. KORBA - P. ZVENGROWSKI ...
Topology and its Applications
Czechoslovak Mathematical Journal
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Czechoslovak Mathematical Journal
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Bulletin of the Belgian Mathematical Society - Simon Stevin
We derive an inequality for the Z 2-cup-length of any smooth closed connected manifold unoriented... more We derive an inequality for the Z 2-cup-length of any smooth closed connected manifold unorientedly cobordant to zero. In relation to this, we introduce a new numerical invariant of a smooth closed connected manifold, called the characteristic rank. In particular, our inequality yields strong upper bounds for the cup-length of the oriented Grassmann manifoldsG n,k ∼ = SO(n)/SO(k) × SO(n − k) (6 ≤ 2k ≤ n) if n is odd; if n is even, we obtain new upper bounds in a different way. We also derive lower bounds for the cup-length ofG n,k. ForG 2 t −1,3 (t ≥ 3) our upper and lower bounds coincide, giving that the Z 2-cup-length is 2 t − 3 and the characteristic rank equals 2 t − 5. Some applications to the Lyusternik-Shnirel'man category are also presented. * This paper is dedicated to the memory of Bob Stong, in thanks for his comments.
Bulletin of the Belgian Mathematical Society - Simon Stevin
Bulletin of the Belgian Mathematical Society - Simon Stevin
Mathematica Slovaca
We present a complete functional formula expressing the
Homology, Homotopy and Applications, 2016
This paper presents a new approach to studying the kernel of the additive homomorphism from H q (... more This paper presents a new approach to studying the kernel of the additive homomorphism from H q (G n,k) to H q+1 (G n,k) given by the cup-product with the first Stiefel-Whitney class of the canonical k-plane bundle over the Grassmann manifold G n,k of all k-dimensional vector subspaces in Euclidean n-space. This method enables us to improve the understanding of the Z 2-cohomology of the "oriented" Grassmann manifold G n,k of oriented k-dimensional vector subspaces in Euclidean n-space. In particular, we derive new information on the characteristic rank of the canonical oriented k-plane bundle over G n,k and the Z 2-cup-length of G n,k. Our results on the cup-length for three infinite families of the manifolds G n,3 confirm the corresponding claims of Fukaya's conjecture from 2008. Dedicated to Professor Ulrich Koschorke on the occasion of his 75-th birthday.
Rendiconti del Circolo Matematico di Palermo (1952 -), 2016
Uploads
Papers by Július Korbaš