Math 690, Section 01, De Rham Homotopy Theory
Fall, 2016
Schedule: 3:05 to 4:20, Tuesdays and Thursdays; Physics 205
Instructor: Richard Hain
References:
- K.-T. Chen: Iterated path integrals, Bull. Amer. Math. Soc. 83 (1977), 831-879. (pdf)
- R. M. Hain: The Geometry of the Mixed Hodge Structure on the Fundamental Group, in Algebraic geometry, Bowdoin, 1985, Proc. Symp. Pure. Math. 46 (1987), pp. 247-282. (pdf)
- R. M. Hain: Big Red , University of Utah preprint, 1984 (unpublished). (pdf)
- J. Milnor, J. Moore: On the structure of Hopf algebras,
Ann. of Math. 81 (1965), 211-264. (pdf)
- D. Quillen: Rational homotopy theory, Ann. of Math. 90 (1969), 205-295.
(pdf)
- E. Spanier: Algebraic topology, McGraw-Hill, 1966. (There is a
more recent corrected version published by Springer.)
Topics:
- Iterated integrals
- Bar constructions and Eilenberg Moore spectral sequences
- Path space de Rham theorems
- Basics of mixed Hodge theory
- Mixed Hodge structures on homotopy groups
- Relative unipotent completion and associated de Rham theorems
- Deligne's canonical extension of a locally unipotent flat connection
- Some ODE + regularization of integrals
- Limit mixed Hodge structures
- Introduction to MMM and universal MEM
Notes:
- Time ordered simplices (pdf)
- Simplicial and cosimplicial objects (pdf)
- The simplicial unit interval (pdf)
- The cosimplicial model of the path space (pdf)
- Fiber integration (pdf)
- Iterated integrals (pdf)
- Product, coproduct and antipode (pdf)
- Odds and ends (pdf)
- Topology (pdf)
- Hopf algebras (pdf)
- Fibrations (pdf)
- Bar constructions (pdf)
- Variations of MHS and limits of periods (pdf)
Return to: Richard Hain *
Duke Mathematics Department *
Duke University