{: .photo }
[Frank Adams] 1930-1989.
[More pictures][adams-pictures]
[Frank Adams]: http://www-groups.dcs.st-andrews.ac.uk/Biographies/Adams_Frank.html
[adams-pictures]: http://www-groups.dcs.st-andrews.ac.uk/history/PictDisplay/Adams_Frank.html
{: .photo }
[Leonhard Euler] 1707-1783.\\
[More pictures][euler-pictures].
Euler is also depicted on an old version of the
[Swiss 10 franc note](http://www2.physics.umd.edu/%7Eredish/Money/euler.jpg).
[Leonhard Euler]: http://www-groups.dcs.st-andrews.ac.uk/Biographies/Euler/
[euler-pictures]: http://www-groups.dcs.st-and.ac.uk/%7Ehistory/PictDisplay/Euler.html
{: .photo }
[Jules Henri Poincaré](
http://www-groups.dcs.st-andrews.ac.uk/Biographies/Poincare/)
1854-1912. [More pictures](http://www-groups.dcs.st-and.ac.uk/%7Ehistory/PictDisplay/Poincare.html).
{: .photo }
Daniel Kan
1927-2013
{: .photo }
[Solomon Lefschetz](
http://www-groups.dcs.st-andrews.ac.uk/Biographies/Lefschetz/)
1884-1972
{: .photo }
[Heinz Hopf](
http://www-groups.dcs.st-and.ac.uk/Biographies/Hopf/)
1891-1971.
{: .photo }
[J. H. C. Whitehead](
http://turnbull.mcs.st-and.ac.uk/Biographies/Whitehead_Henry/)
1904-1960
{: .photo }
[Norman Earl Steenrod](
http://www-groups.dcs.st-andrews.ac.uk/Biographies/Steenrod/)
1910-1971
{: .photo }
[Samuel Eilenberg](
http://www-groups.dcs.st-andrews.ac.uk/Biographies/Eilenberg/)
1913-1998
## Instructor Information
* [Doug Ravenel](/people/faculty/doug/) : Office hours: TBA [Zoom link](https://rochester.zoom.us/j/5775049882)
## Class meetings
* MW 2:00-3:15 in Hylan 1104. [Live Zoom link](https://rochester.zoom.us/s/99804485280)
* The first and last meetings will be on Wednesday August 26 and December 9.
* There will be no classes on Monday September 2 (Labor Day), October
14 (Fall break) and November 27 (Thanksgiving break).
* I will be out of town on October 16 and December 9. We will find a way to make up those two classes.
* [Lecture notes](notes/)
* [Homework](homework/)
* [Textbook and course introduction](course/)
* The final exam will be on TBA
* [Course evaluation
link](http://www.rochester.edu/registrar/course-evaluations.html)
## Handouts
* [Cohomology operations and applications in
homotopy
theory](https://people.math.rochester.edu/faculty/doug/mypapers/mosher-tangora.pdf) by Robert Mosher and Martin Tangora, 1968.
A very helpful book based on lectures given by Frank Peterson at MIT.
* [Doug's Kervaire invariant
page](https://people.math.rochester.edu/faculty/doug/kervaire.html).
Includes link to the purple book, Equivariant stable homotopy theory
and the Kervaire invariant, with Mike Hill and Mike Hopkins.
* [Prepublication draft of the purple book](https://people.math.rochester.edu/faculty/doug/mybooks/esht-new.pdf).
* [Slides](https://people.math.rochester.edu/faculty/doug/Talks/Regensburg-talk.pdf)
for Doug's recent talk ""What is an ∞-category?" [Paper based on
this talk](https://people.math.rochester.edu/faculty/doug/mypapers/gjm-cat.pdf).
* [Simplicial sets, Section 3.4A of the purple book](simp-sets.pdf).
* [Ends and coends, Section 2.4 of the purple book](coends.pdf).
* [Answer sheet for 2012 final exam.](final-12-soln.pdf)
* [Answer sheet for 2013 final exam.](final-13-soln.pdf)
* [Answer sheet for Spring 2014 final exam.](final-14-soln.pdf)
* [Answer sheet for Fall 2014 final exam.](final-14f.pdf)
* [Answer sheet for Fall 2015 final exam.](final-15-soln.pdf)
* [Answer sheet for Fall 2016 final exam.](final-16-soln.pdf)
* [Answer sheet for Fall 2017 final exam.](final-17-sol.pdf) Note to self: this exam was TOO EASY.
* [Answer sheet for Fall 2019 final exam.](final-19-sol.pdf)
* [Fall 2020 final exam.](f20final.pdf) [Answer sheet](f20final-sol.pdf).
* [Fall 2021 final exam.](f21final.pdf) [Answer sheet](f21final-sol.pdf).
* [Fall 2022 final exam.](f22final.pdf) [Answer sheet](f22final-sol.pdf).
* [An Introduction to Algebraic Topology](rotman.pdf) by Joseph
J. Rotman, our textbook.
## Links
* Videos by Jos Leys
* [From an ocatagon to a genus 2 surface](https://www.youtube.com/watch?v=G1yyfPShgqw&list=RDCMUC6YBBZzT2KURLjiOJBgGGOg&index=2).
* [From an 40-gon to a genus 10
surface](https://www.youtube.com/watch?v=RBWwlfcftYM).
* [The Boy surface](https://www.youtube.com/watch?v=uiq-EcQz_uU&t=2s)
* [The cross-cap](https://www.youtube.com/watch?v=W-sKLN0VBkk&t=2s)
* [The double-tipping null homotopy by David Pengelley and Daniel
Ramras.](http://www.math.iupui.edu/~dramras/double-tip.html) A
detailed explanation of the coffee cup and belt tricks, with links to
a paper and several videos.
* [HOMOTOPY THEORY FOR BEGINNERS](http://www.math.ku.dk/~moller/e01/algtopI/comments.pdf) (comments to Chapter 0 of Hatcher's book)
* [THE FUNDAMENTAL GROUP AND COVERING SPACES](
http://www.math.ku.dk/~moller/f03/algtop/notes/covering.pdf)
and
[From singular chains to Alexander Duality](
http://www.math.ku.dk/~moller/f03/algtop/notes/homology.pdf)
by
[JESPER M. MØLLER](http://www.math.ku.dk/~moller/).
* [Biographies of mathematicians](
http://www-groups.dcs.st-andrews.ac.uk/history/BiogIndex.html)
* [A history of Topology](
http://www-groups.dcs.st-andrews.ac.uk/history/HistTopics/Topology_in_mathematics.html)
* [Other books and courses on algebraic topology](others.html)
* [The seven bridges of Königsberg
](seven.html)
{: .inline-photo }
* [
Platonic solids and Euler's number
](http://en.wikipedia.org/wiki/Platonic_solid)
{: .inline-photo }
* [
Stellations of Platonic solids
](stellations.html)
{: .inline-photo }
* [
Twenty Proofs of Euler's Formula: V-E+F=2
](http://www.ics.uci.edu/~eppstein/junkyard/euler/)
{: .inline-photo }
* [
A Proof of Euler's Formula
](http://math.rice.edu/%7Epcmi/sphere/gos6.html)
{: .inline-photo }
* [
THE MÃBIUS BAND
](http://neil-strickland.staff.shef.ac.uk/courses/algtop/pictures/mobius/)
{: .inline-photo }
* [Everting the sphere (turning it inside out)
](evert.html)
{: .inline-photo }
* [
The Klein bottle
](bottle.html)
{: .inline-photo }
* [The Boy surface
](boy.html)
{: .inline-photo }
* [
Math That Makes You Go Wow: A Multi-Disciplinary Exploration of
Non-Orientable Surfaces
](http://www.math.ohio-state.edu/~fiedorow/math655/yale/)
Undergraduate math appreciation course at Yale, 1998.
{: .inline-photo }
* [
The Hopf fibration
](hopf.html)
The discovery of this map by
[Heinz Hopf](http://en.wikipedia.org/wiki/Heinz_Hopf)
in 1930 marks the beginning of homotopy theory.
{: .inline-photo }
* [
Miscellany
](misc.html)
Other cool links not in the above categories.
{: .inline-photo }
* [Some papers on Platonic surfaces](Platonicpapers.html)
* [Links for three and four dimensional polyhedra](polyhedra.html)