MATH 443

Frank Adams 1930-1989. More pictures

Leonhard Euler 1707-1783.
More pictures. Euler is also depicted on an old version of the Swiss 10 franc note.

Jules Henri Poincaré 1854-1912. More pictures.

Daniel Kan 1927-2013

Solomon Lefschetz 1884-1972

Heinz Hopf 1891-1971.

J. H. C. Whitehead 1904-1960

Norman Earl Steenrod 1910-1971

Samuel Eilenberg 1913-1998

Instructor Information

• Doug Ravenel : Office hours: TBA

Class meetings

• MW 2:00-3:15 in Hylan 1104.

• 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

• Homework

• Textbook and course introduction

• The final exam will be on TBA

• Course evaluation link

Handouts

• Doug’s Kervaire invariant page. 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.

• Slides for Doug’s recent talk ““What is an ∞-category?” Paper based on this talk.

• Simplicial sets, Section 3.4A of the purple book.

• Ends and coends, Section 2.4 of the purple book.

• Answer sheet for 2012 final exam.

• Answer sheet for 2013 final exam.

• Answer sheet for Spring 2014 final exam.

• Answer sheet for Fall 2014 final exam.

• Answer sheet for Fall 2015 final exam.

• Answer sheet for Fall 2016 final exam.

• Answer sheet for Fall 2017 final exam. Note to self: this exam was TOO EASY.

• Answer sheet for Fall 2019 final exam.

• Fall 2020 final exam. Answer sheet.

• Fall 2021 final exam. Answer sheet.

• Fall 2022 final exam. Answer sheet.

• An Introduction to Algebraic Topology by Joseph J. Rotman, our textbook.

Links

• Videos by Jos Leys
  • From an ocatagon to a genus 2 surface.
  • From an 40-gon to a genus 10 surface.
  • The Boy surface
  • The cross-cap

• The double-tipping null homotopy by David Pengelley and Daniel Ramras. A detailed explanation of the coffee cup and belt tricks, with links to a paper and several videos.

• HOMOTOPY THEORY FOR BEGINNERS (comments to Chapter 0 of Hatcher’s book)

• THE FUNDAMENTAL GROUP AND COVERING SPACES and From singular chains to Alexander Duality by JESPER M. MØLLER.

• Biographies of mathematicians

• A history of Topology

• Other books and courses on algebraic topology

• The seven bridges of Königsberg

• Platonic solids and Euler’s number

• Stellations of Platonic solids

• Twenty Proofs of Euler’s Formula: V-E+F=2

• A Proof of Euler’s Formula

• THE MÖBIUS BAND

• Everting the sphere (turning it inside out)

• THE KLEIN BOTTLE

• Boy’s surface

• Math That Makes You Go Wow: A Multi-Disciplinary Exploration of Non-Orientable Surfaces Undergraduate math appreciation course at Yale, 1998.

• The Hopf fibration The discovery of this map by Heinz Hopf in 1930 marks the beginning of homotopy theory.

• Miscellany Other cool links not in the above categories.

• Some papers on Platonic surfaces

• Links for three and four dimensional polyhedra