### Lectures

**Lecture 1**: Models in Homotopy Theory. Summary Talk**Lecture 2**: Algebraic Models in Rational Homotopy Theory. Summary Talk**Lecture 3**: Algebraic Models in*p*-adic Homotopy Theory. Summary Talk**Lecture 4**: Algebraic Models for Integral Homotopy Types. Summary Talk### Sample Problems

- Some exercises on model categories and rational homotopy theory. pdf
### References

- This list is very incomplete; it just contains the papers and books I may
have mentioned in the talks.

**Lecture 1****Lecture 2**- Quillen, Daniel. Rational homotopy theory, 1969. MR Paper
- Sullivan, D. Differential forms and the topology of manifolds (Tokyo 1973), 1975 MR
- Sullivan, Dennis. Infinitesimal computations in topology, 1977. MR Paper
- Bousfield, A. K. The localization of spaces with respect to homology, 1975. MR Paper
- Hirschhorn, Philip S. Model categories and their localizations, 2003. MR Book
- Bousfield, A. K.; Gugenheim, V. K. A. M. On PL de Rham theory and rational homotopy type, 1976. MR Book
- Mandell, Michael A. Cochain multiplications, 2002. MR Paper

**Lecture 3**- Mandell, Michael A.
*E*_{∞}algebras and*p*-adic homotopy theory, 2001. MR Paper (Use this link; the published version was mangled by the publisher.) - Miller, Edward Y. de Rham cohomology with arbitrary coefficients, 1978. MR Paper
- Hinich, V. A.; Schechtman, V. V. On homotopy limit of homotopy algebras, 1987. MR Paper
- McClure, James E.; Smith, Jeffrey H. Multivariable
cochain operations and little
*n*-cubes, 2003. MR Paper - Berger, Clemens; Fresse, Benoit. Combinatorial operad actions on cochains, 2004. MR Paper

- Mandell, Michael A.
**Lecture 4**- Mandell, Michael A. Cochains and homotopy type, 2006. MR Paper
- Dwyer, W. G.; Kan, D. M. Simplicial localizations of categories, 1980. MR Paper
- Dwyer, W. G.; Kan, D. M. Calculating simplicial localizations, 1980. MR Paper
- Dwyer, W. G.; Kan, D. M. Function complexes in homotopical algebra, 1980. MR Paper
- Mandell, Michael A. Equivalence of simplicial localizations of closed model categories, 1999. MR Paper
- Ranicki, A. A. Algebraic
*L*-theory and topological manifolds, 1992. MR

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