32 citations · 47 across the 11 of their papers we have counts for
10 papers · 1 filter
Lower bounds on the number of homotopy types of -gauge groups over spheres
Martin Frankland, Yang Hu
We explore the classical question of enumerating the homotopy types of gauge groups of principal -bundles over in the unstable range . Using com…
Multiparameter persistence modules in the large scale
Martin Frankland, Donald Stanley
A persistence module with discrete parameters is a diagram of vector spaces indexed by the poset . If we are only interested in the large scale behavior of such a…
On good morphisms of exact triangles
J. Daniel Christensen, Martin Frankland
In a triangulated category, cofibre fill-ins always exist. Neeman showed that there is always at least one "good" fill-in, i.e., one whose mapping cone is exact. Verdier constructe…
Eilenberg-MacLane mapping algebras and higher distributivity up to homotopy
Hans-Joachim Baues, Martin Frankland
Primary cohomology operations, i.e., elements of the Steenrod algebra, are given by homotopy classes of maps between Eilenberg--MacLane spectra. Such maps (before taking homotopy c…
A user's guide: Completed power operations for Morava -theory
Martin Frankland
The user's guide provides a behind-the-scenes look at the paper of that title.
2-track algebras and the Adams spectral sequence
Hans-Joachim Baues, Martin Frankland
In previous work of the first author and Jibladze, the -term of the Adams spectral sequence was described as a secondary derived functor, defined via secondary chain complexes…
Completed power operations for Morava E-theory
Tobias Barthel, Martin Frankland
We construct and study an algebraic theory which closely approximates the theory of power operations for Morava E-theory, extending previous work of Charles Rezk in a way that take…
The realizability of operations on homotopy groups concentrated in two degrees
Hans-Joachim Baues, Martin Frankland
The homotopy groups of a space are endowed with homotopy operations which define the Π-algebra of the space. An Eilenberg-MacLane space is the realization of a Π-algebra concentrat…
Moduli spaces of 2-stage Postnikov systems
Martin Frankland
Using the obstruction theory of Blanc-Dwyer-Goerss, we compute the moduli space of realizations of 2-stage Pi-algebras concentrated in dimensions 1 and n or in dimensions n and n+1…
Behavior of Quillen (co)homology with respect to adjunctions
Martin Frankland
This paper aims to answer the following question: Given an adjunction between two categories, how is Quillen (co)homology in one category related to that in the other? We identify…