2 citations · 3 across the 7 of their papers we have counts for
10 papers · 1 filter
Evaluation Maps in Rational Homotopy
Yves Felix, Gregory Lupton
Let E be an H-space acting on a based space X. Then we refer to ev: E -> X, the map obtained by acting on the base point of X, as a ``generalized evaluation map." We establish seve…
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…
Rank of the fundamental group of a component of a function space
Gregory Lupton, Samuel Bruce Smith
We compute the rank of the fundamental group of an arbitrary connected component of the space map(X, Y) for X and Y nilpotent CW complexes with X finite. For the general component…
Rationalized Evaluation Subgroups of a Map II: Quillen Models and Adjoint Maps
Gregory Lupton, Samuel Bruce Smith
Let w: Map(X,Y;f) -> Y denote a general evaluation fibration. Working in the setting of rational homotopy theory via differential graded Lie algebras, we identify the long exact se…
Rationalized Evaluation Subgroups of a Map and the Rationalized G-Sequence
Gregory Lupton, Samuel Bruce Smith
Let f: X -> Y be a based map of simply connected spaces. The corresponding evaluation map w: map(X,Y;f) -> Y induces a homomorphism of homotopy groups whose image in pi_n(Y) is cal…
Cyclic Maps in Rational Homotopy Theory
Gregory Lupton, Samuel Bruce Smith
The notion of a cyclic map g: A -> X is a natural generalization of a Gottlieb element in pi_n(X). We investigate cyclic maps from a rational homotopy theory point of view. We show…