Jeffrey Strom

The Lusternik-Schnirelmann category of Sp(3)

We show that the Lusternik-Schnirelmann category of the symplectic group Sp(3) is 5. This L-S category coincides with the cone length and the stable weak category.

The sectional category of a map

We study a generalization of the Svarc genus of a fibre map. For an arbitrary collection ɛ of spaces and a map f : X → Y , we define a numerical invariant, the ɛ-sectional category of f , in terms of open covers of Y . We obtain several basic properties of ɛ-sectional category, including those dealing with homotopy domination and homotopy pushouts. We then give three simple axioms which characterize the ɛ-sectional category. In the final section, we obtain inequalities for the ɛ-sectional category of a composition and inequalities relating the ɛ-sectional category to the Fadell–Husseini category of a map and the Clapp–Puppe category of a map.

Idempotent functors that preserve cofiber sequences and split suspensions

We show that an

Implications of the Ganea condition

f

Modern Classical Homotopy Theory

-localization functor

Lusternik-Schnirelmann category of spaces with free fundamental group

L_f

Finite-dimensional spaces in resolving classes

commutes with cofiber sequences of

Miller spaces and spherical resolvability of finite complexes

(N-1)

Homotopy classes of self-maps and induced homomorphisms of homotopy groups

-connected finite complexes if and only if its restriction to the collection of

Limits and colimits

(N-1)