We give conditions when cat(f Ã— g) < cat(f) + cat(g). We apply our result to show that under suitable conditions for rational maps f , mcat(f) < cat(f) is equivalent to cat(f) = cat(fÃ—idSn). Manyâ€¦ (More)

Closed model categories are a general framework introduced by Quillen [15] in which one can do homotopy theory. An alternative framework has been developed by Baues [2]. Putting a closed modelâ€¦ (More)

It is proved that the cone length or strong category of a product of two co-H-spaces is less than or equal to two. This yields the following positive solution to a problem of Ganea: Let Î± âˆˆ Ï€2p(S) beâ€¦ (More)

Given a graph, suppose that intruders hide on vertices or along edges of the graph. The fast searching problem is to find the minimum number of searchers required to capture all intruders satisfyingâ€¦ (More)

For any collection of spaces A, we investigate two non-negative integer ho-motopy invariants of maps: L A (f), the A-cone length of f , and L A (f), the A-category of f. When A is the collection ofâ€¦ (More)

Suppose the spacesX andX A have the same Lusternik-Schnirelmann category: cat(X A) = cat(X). Then there is a strict inequality cat(X (AoB)) < cat(X) + cat(AoB) for every space B, provided theâ€¦ (More)

Let the circle act effectively in a Hamiltonian fashion on a compact symplectic manifold (M, Ï‰). Assume that the fixed point set M 1 has exactly two components, X and Y , and that dim(X) + dim(Y ) +â€¦ (More)

We have previously demonstrated that intracisternal (i.c.) administration of neurotensin (NT), a brain and gastrointestinal tridecapeptide, potently inhibits gastric ulcer formation induced byâ€¦ (More)