With motivation from algebraic topology, algebraic geometry, and string
theory, we study various topics in differential homological algebra.
The work is divided into five largely independent Parts:
In differential algebra, operads are systems of parameter chain complexes
for multiplication on various types of differential graded algebras
"up to homotopy", for example commutative algebras, n-Lie algebras,
n-braid algebras, etc. Our primary focus is the development of the
concomitant theory of modules up to homotopy and the study of both classical
derived categories of modules over DGA's and derived categories of modules
up to homotopy over DGA's up to homotopy. Examples of such derived
categories provide the appropriate setting for one approach to mixed Tate
motives in algebraic geometry, both rational and integral.
This monograph will appear in Asterisque.
Here is a pointer to the
Here is a pointer to the paper at Purdue.