GADGET Seminar (Fall 2008)
Announcements
Basic Information
Meetings: Tuesdays 12:30-2:00, RLM
9.166
Resources
Introduction to simplicial sets
(G. Friedman)
Lectures on simplicial sets (M. Hopkins):
brief intro,
1,
2,
3,
4,
5,
6
Book on simplicial homotopy theory
(Goerss-Jardine). Chapter 1 contains theory of simplicial sets
Notes on simplicial sets (R. Bott). Here they are
called "semi-simplicial sets" and these notes contain much more.
Lecture on Dold-Kan (M. Hopkins)
The book "An introduction to homological algebra" by C. Weibel contains a
chapter on simplicial sets and the Dold-Kan theorem
Lectures on categories (M. Hopkins):
1,
2
What is an infinity category?
(J. Lurie)
Notes on quasicategories (= infinity
categories) (M. Boyarchenko)
Summer school notes on
interactions between homotopy theory and algebra. In particular Hess' notes
are on rational homotopy theory.
Lectures on model categories (M. Hopkins):
1,
2
Lectures on rational homotopy theory (M. Hopkins):
1,
2,
3,
4,
5,
6
Homotopical algebra (djvu file)
(D. Quillen)
Rational homotopy theory (D. Quillen)
Infinitesimal computations in topology
(D. Sullivan)
Rational homotopy theory and differential forms (djvu file)
(P. Griffiths, J. Morgan)
Geometric topology:
localization, periodicity and Galois symmetry (D. Sullivan)
Felix, Yves; Halperin, Stephen; Thomas, Jean-Claude Rational homotopy
theory. Graduate Texts in Mathematics, 205. Springer-Verlag, New York,
2001.
Quillen, Daniel, On the (co-) homology of commutative rings. 1970
Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVII, New
York, 1968) pp. 65--87.