

Simplicial and Cosimplicial Methods

By simplicial methods, we mean the method of studying
geometric or algebraic objects by using simplicial
objects in those categories. A classical textbook is
the book
[
May92
]
by Peter May. Another classical one is Curtis’s
[
Cur71
]
. The famous book
[
BK72
]
by Bousfield and Kan can be used as a practical
textbook to learn how to use simplicial sets. A modern
treatment is given in the book
[
GJ99
]
by Goerss and Jardine.
Those who love abstract cocepts can start with the
definition of simplicial objects. Most people would
feel comfortable, however, if he/she learn simplicial
sets as an abstraction of simplicial complexes.
Dwyer’s text in
[
DH01
]
and Friedman’s
[
Fri
]
can serve as good introductory texts for this
purpose.
[BK72]
A. K. Bousfield and D. M. Kan.
Homotopy limits, completions
and localizations
, volume 304 of
Lecture Notes in Mathematics
. SpringerVerlag, Berlin, 1972. 2nd corrected
printing 1987.
[Cur71]
Edward B. Curtis. Simplicial homotopy theory.
Advances in Math.
, 6:107–209 (1971), 1971.
[DH01]
William G. Dwyer and HansWerner Henn.
Homotopy
theoretic methods in group cohomology
. Advanced Courses in Mathematics—CRM
Barcelona. Birkhèˆ«ser Verlag, Basel, 2001.
[Fri]
Greg Friedman. An elementary illustrated
introduction to simplicial sets,
arXiv:0809.4221
.
[GJ99]
J. Peter May.
Simplicial objects in algebraic topology
. Chicago Lectures in Mathematics. University of
Chicago Press, Chicago, IL, 1992.


