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Digital Cofibration and Digital Lusternik-Schnirelmann Category in the Sense of Subdivision
In this paper, using the notion of subdivision, the authors generalize the definition of cofibration in digital topology and show that this kind of...
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On Real Flag Manifolds with Cup-Length Equal to Its Dimension
We prove that for any positive integers n 1 , n 2 ,…, n k , there exists a real flag manifold F (1,…, 1, n 1 , n 2 , …, n k ) with cup-length equal to its...
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On the cup-length of certain classes of flag manifolds
We compute the cup-length of flag manifolds F (2, 2, n 3 ) and F (1, 3, 2 s +1 − 3) and the height of the third Stiefel–Whitney characteristic class of the...
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Inductive LS cocategory and localisation
In this paper we prove that the inductive cocategory of a nilpotent CW -complex of finite type X , indcocat X , is bounded above by an expression...
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Trace map, Cayley transform and LS category of Lie groups
The aim of this article is to use the so-called Cayley transform in order to compute the LS category of Lie groups and homogeneous spaces by giving...
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Morse–Bott functions and the Lusternik–Schnirelmann category
Lusternik–Schnirelmann category of a manifold gives a lower bound of the number of critical points of a differentiable map on it. The purpose of this...
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Effect of topology on the multiplicity of solutions for some semilinear elliptic systems with critical Sobolev exponent
In this paper, we are concerned with the effect of the domain topology on the multiplicity of solutions for some semilinear elliptic systems...
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A n theory, L.S. category, and strong category
Relations between category and strong category are studied. The notion of a homotopy coalgebra of order r over the Ganea comonad is introduced. It is...
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Lagrangian intersections, critical points and Qcategory
For a manifold M , we prove that any function defined on a vector bundle of basis M and quadratic at infinity has at least Qcat ( M )+1 critical points....
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L-S Categories of Simply-connected Compact Simple Lie Groups of Low Rank
We determine the L-S category of Sp(3) by showing that the 5-fold reduced diagonal Δ5 is given by V 2using a Toda bracket and a...
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Seifert unions of solid tori
We obtain a list of all 3-manifolds that can be obtained by gluing 3-balls and solid tori along mutually disjoint surfaces in their boundaries.
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Model Categories in Algebraic Topology
This survey of model categories and their applications in algebraic topology is intended as an introduction for non homotopy theorists, in particular...
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Singhof fillings of closed 3-manifolds
We give a complete classification of all closed, connected 3-manifolds which admit a Singhof filling with any number of solid tori.
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Cochain model for thickenings and its application to rational LS-category
A thickening of a finite CW-complex X is by definition a compact manifold M of the same simple homotopy type as X . We give a model for the cochain...
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Lower bounds¶for the relative Lusternik–Schnirelmann category
We give estimates of numerical homotopy invariants of the pair ( X , X × S p ) in terms of homotopy invariants of X . More precisely, we prove that σ ...
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Equivalent definitions of the Ganea fibrations¶and cofibrations
The Ganea fibrations have been used to define Lusternik–Schnirelmann category. It is proved that three definitions of the Ganea fibrations are...