Homotopy Groups of H-Spaces I
Homotopy groups of small categories and derived functors
Homotopy Lie algebras and fundamental groups via deformation theory
We formulate first results of our larger project based on first fixing some easily accessible invariants of topological spaces (typically the cup product structure in low dimensions) and then studying the variations of more complex invariants such as (the homotopy Lie algebra) or (the graded Lie algebra associated to the lower central series of the fundamental group). We prove basic rigidity results and give also an application in low-dimensional topology.
Homotopy Lie algebras; lower central series and the Koszul property.
Homotopy nilpotent Lie groups have no torsion in homology.
Homotopy over and under
Homotopy sequences of fibrations
Homotopy theory of the master equation package applied to algebra and geometry: a sketch of two interlocking programs
Using the algebraic theory of homotopies between maps of dga's we obtain a homotopy theory for algebraic structures defined by collections of multiplications and comultiplications. This is done by expressing these structures and resolved versions of them in terms of dga maps. This same homotopy theory of dga maps applies to extract invariants beyond homological periods from systems of moduli spaces that determine systems of chains that satisfy master equations like dX + X*X = 0. Minimal models of...
Homotopy types of one-dimensional Peano continua
Let X and Y be one-dimensional Peano continua. If the fundamental groups of X and Y are isomorphic, then X and Y are homotopy equivalent. Every homomorphism from the fundamental group of X to that of Y is a composition of a homomorphism induced from a continuous map and a base point change isomorphism.
Hurewicz Theorems for Pairs and Squares.
Hybrid Reduced and Symmetric Product Spaces.