7 citations · 13 across the 7 of their papers we have counts for
8 papers
Binary Operations for Homotopy Groups with Coefficients
Martin Arkowitz
We define and study binary operations for homotopy groups with coefficients. We give conditions to prove that certain binary operations are the homomorphic image of the generalized…
Homotopy Actions, Cyclic Maps and their Duals
Martin Arkowitz, Gregory Lupton
An action of A on X is a map F: AxX to X such that F|_X = id: X to X. The restriction F|_A: A to X of an action is called a cyclic map. Special cases of these notions include group…
The cone length and category of maps: pushouts, products and fibrations
Martin Arkowitz, Donald Stanley, Jeffrey Strom
For any collection of spaces A, we investigate two non-negative integer homotopy 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…
The Lefschetz-Hopf theorem and axioms for the Lefschetz number
Martin Arkowitz, Robert F. Brown
The reduced Lefschetz number, that is, the Lefschetz number minus 1, is proved to be the unique integer-valued function L on selfmaps of compact polyhedra which is constant on homo…
The sectional category of a map
Martin Arkowitz, Jeffrey Strom
We study a generalization of the Svarc genus of a fiber map. For an arbitrary collection E of spaces and a map f:X-->Y, we define a numerical invariant, the E-sectional category of…
Homotopy classes that are trivial mod F
Martin Arkowitz, Jeffrey Strom
If F is a collection of topological spaces, then a homotopy class αin [X,Y] is called F-trivial if α_* = 0: [A,X] --> [A,Y] for all A in F. In this paper we study the collection Z_…