2 citations · 2 across the 4 of their papers we have counts for
4 papers
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…