Algebraic Models For Homotopy Types
Minicourse at EPFL for Young Topologists
Meeting 2013
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
- Quillen, Daniel G. Homotopical algebra, 1967.
MR
Book
- Dwyer, W. G.; Spaliński, J. Homotopy theories and
model categories, 1995.
MR
Paper
- Hovey, Mark. Model categories, 1999.
MR
Book
- 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
- 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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