Course description by Dennis

Video of Lecture 1/4 (Dennis, 18.12.2013)

Video of Lecture 2/4 (Anibal, 9.1.2014)

Video of Lecture 3/4 (Dennis, 16.1.2014)

Video of Lecture 4/4 (Anibal, 23.1.2014)

Background: The Poincare duality theorem and its converse Slides of two lectures by A.R. (Bochum, December 2011)

An intercontinental 4-part lecture series on the total surgery obstruction given by A.R. Part 1, Part 2 (Stony Brook, 18.4.2014), Part 3, Part 4 (Edinburgh, 2.5.2014)

Even-dimensional l-monoids and L-theory, Algebraic and Geometric Topology 7, 479-515 (2007)

Proper surgery groups and Wall-Novikov groups, by Serge Maumary, Vol. III Proc. Algebraic K-theory,Battelle, Seattle, Springer Lecture Notes 343, 526--529 (1974)

Larry Siebenmann's thesis (Princeton, 1965). Retyped LATEX version.

Notes of Warwick course (1966) (by Rainer Vogt).

J.Cerf

A.Haefliger

M.Kervaire

S.Smale

Retyped version (2010) by Shu Otsuka (with some additional material).

Basis for the Milnor-Stasheff book

zipped DJVU, PDF, readme by Larry Siebenmann.

The book (modulo the comments in the MacTutor biography) contains the first modern proof of the classification of surfaces.

The book includes on page 151 the celebrated picture of Bessel-Hagen, to whom there is a reference on page 267. Apparently there was a bet that Kerekjarto would put a reference to Bessel-Hagen in the book. A sad example of mathematical humour.

The signature of a 4k-dimensional manifold was first defined in this paper (on the last page).

The paper was written in Spanish and published in Mexico since at the time algebraic topology was regarded as a somewhat shameful activity, and Weyl did not want his colleagues in Zürich to know about his contributions to the subject!

Information from Beno Eckmann's lecture Is algebraic topology a respectable field? (Mathematical Survey Lectures, Springer, 2006).

The original article (W.Boy, Über die Curvatura integra und die Topologie geschlossener Flächen, Math. Ann. 57 (1903), 151-184). Obituary of Boy (1879-1914).

What is ... Boy's surface? (Rob Kirby, Notices of AMS 54 (2007), 1306-1307).

An embedding of a topologist in the Oberwolfach metal model of Boy's immersion made at the Mercedes-Benz factory in Stuttgart.

Bernard Morin, the blind French topologist, visited Oberwolfach shortly after the installation of the Boy's immersion model -- he walked around it, feeling its edges, and then declared that this was not the original Boy's immersion but its mirror image!

Cobordism of immersions by R.Wells (Topology 5, 281--294, 1966).

The cobordism group of immersed surfaces in $R3$ is isomorphic to the cyclic group $Z$

Generalizations of the Kervaire invariant by E.H.Brown (Annals of Mathematics 95, 368--383, 1972).

Example 1.28 shows that the isomorphism is defined by the $Z$

8 Boys bound Movie made by Tony Phillips, with supplementary material.

The movie illustrates Boy's immersion of the projective plane in $R3$, which generates the cobordism group, and how to bound 8 copies of it.

Note that 4 copies bound the immersion of the torus in $R3$ with nontrivial $Z$

Boy's Surface Another YouTube movie..

Sur les immersions de Boy by J. Lannes, Algebraic topology, Aarhus 1982, Springer Lecture Notes 1051, 263--270 (1984)

La surface de Boy by F.Apery, Adv. in Math. 61, 185-266 (1986). Exhibits the Boy immersion as a real algebraic surface.

Poincaré website (in French, 2017)

An essentially topological account of Stokes' theorem, using the first (

See also Iron Rings, Doctor Honoris Causa Raoul Bott, and a Hidden Hand by P.R.Kotiuga (2010)