Books, papers, videos, theses, notes, links etc.
YouTube collections of videos by Carmen Rovi
Many are of surgery-related lectures (2012-)
A note on characteristic classes:
Euler, Stiefel-Whitney, Chern and Pontrjagin (2016)
A construction of Seifert surfaces by differential geometry,
Edinburgh Ph.D. thesis of Supreedee Dangskul (2015)
E_\infty-Comodules and Topological Manifolds,
Stony Brook Ph.D. thesis of Anibal Medina (2015)
Some applications of algebraic surgery
theory: 4-manifolds, triangular matrix rings and braids,
Edinburgh Ph.D. thesis of Chris Palmer (2015)
The signature modulo 8 of fibre bundles, Edinburgh Ph.D. thesis of
Carmen Rovi (2015)
Double L-theory Edinburgh Ph.D. thesis of Patrick Orson (2015)
Algebraic K-Theory and Manifold Topology. Notes
of Jacob Lurie's 2014 Harvard course.
The hotel of algebraic surgery Bonn Ph.D. thesis of Philipp Kuehl (2014).
Minicourse on Topological Manifolds by Dennis Sullivan and Anibal Medina (Stony Brook, December 2013 - January 2014)
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 2 (Stony Brook, 18.4.2014),
Homeomorphisms, homotopy equivalences and chain complexes
Edinburgh Ph.D. thesis of Spiros Adams-Florou (2012). arXiv:1205.3024
On the concordance orders of knots
Edinburgh Ph.D. thesis of Julia Collins (2012). arXiv:1206.0669
A second order algebraic knot concordance group
Edinburgh Ph.D. thesis of Mark Powell (2011).
The total surgery obstruction revisited
by P.Kuehl, T.Macko and A.Mole arXiv:1104.50 (2011)
The Manifold Atlas Project.
Algebraic L-theory and surgery. Notes
of Jacob Lurie's 2011 Harvard course.
Scholarpedia article (2010) by S.P.Novikov on the Novikov conjecture.
Norman Levitt (1943-2009)
Post to the ALGTOP-L algebraic topology discussion forum,
and text spoken at memorial service.
Topics in geometric topology. Notes
of Jacob Lurie's 2009 Harvard course.
The topological rigidity of the torus,
essay written by Alexandre Martin (a student at ENS, Paris) during a visit to Edinburgh February-June 2009.
Slides of talk.
Algebraic and geometric surgery Notes by Adam Mole of course given by A.R. (Muenster, 2008)
Waldhausen's topology lecture notes (Bielefeld, 2005)
On the signature of fibre bundles and absolute Whitehead torsion. Edinburgh Ph.D. thesis of Andrew Korzeniewski (2005)
Splitting homotopy equivalences along codimension 1 submanifolds. Edinburgh Ph.D. thesis of
Jeremy Brookman (2004)
The algebraic theory of Kreck surgery. Edinburgh Ph.D. thesis of
Joerg Sixt (2004)
Even-dimensional l-monoids and L-theory, Algebraic and Geometric Topology 7, 479-515 (2007)
The surgery theoretic classification of high-dimensional smooth and piecewise linear simply-connected manifolds
Harvard senior thesis of Jonathan Kelner (2002)
The mapping torus (entry in Online
Encyclopedia of Mathematics) (2002)
Slice knots: Knot theory in dimension 4. Lecture notes of 2001 UCSD course of Peter Teichner, edited by Julia Collins and Mark Powell.
Invariants of boundary link cobordism. Edinburgh Ph.D. thesis of
Des Sheiham (2001).
An introduction to algebraic surgery in Surveys on Surgery Theory, Vol. 2, Annals of Mathematics Studies 149, 81--163, Princeton (2001)
Foundations of algebraic surgery Another (and shorter) introduction, which appeared in the Proceedings of the School on High-dimensional Manifold Topology, ICTP Trieste, 21 May - 8 June, 2001
Fundamental domains of infinite cyclic covers.
Edinburgh M.Phil thesis of Adam Hughes (2000)
Cobordism and exotic spheres
Harvard senior thesis of Joshua Plotkin (1999)
A letter to Frank Connolly
A letter written in April 1996, on the elements of order 4 in UNil_3(Z).
Nil-groups and regularity
An unpublished paper of Pierre Vogel, with an erratum for Theorem 5-4 (1990)
John Frank Adams. 5 November 1930-7 January 1989
by I.M.James, Biographical Memoirs of Fellows of the Royal Society, Vol. 36 (Dec., 1990), pp. 3-16
An explicit projection
An unpublished paper giving an explicit example of a f.g. projective module over a finite group ring which is not stably f.g. free.
Proceedings of Conference on Algebraic and Geometric Topology, Rutgers, 1983
Springer Lecture Notes 1126, 318--419 (1985)
A letter to Bruce Williams
A letter written in December 1981, on the relationship between projective,
free and simple L-groups.
Z_2-homotopy theory by Michael Crabb,
LMS Lecture Notes 44 (1980)
Localization of spaces with respect to a class of maps by Pierre Vogel,
Nantes notes (1978)
Surgery on closed manifolds, Larry Taylor and Bruce Williams,
Notre Dame notes (ca. 1977)
Topology by J.F. Adams and A.R. Pears,
survey in Use of mathematical literature, 217--228, Butterworths (1977)
Varietes simpliciales d'homologie et varietes topologique metrisables
by Takao Matumoto, Orsay Ph.D. thesis (1976)
Proper surgery groups for non-compact manifolds of finite dimension
Unpublished 1972 paper of Serge Maumary.
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)
Notes of Quillen's 1973 MIT lecture course on algebraic K-theory
Higher algebraic K-theory I.
by Dan Quillen. Proc. Algebraic K-theory Battelle, Seattle Conference, Vol. I.,
Springer Lecture Notes 341, 85-147 (1973)
Surgery on paracompact manifolds
1972 Berkeley Ph.d. thesis of Larry Taylor
Surgery on simply-connected manifolds
The classic book by W.Browder, originally published by Springer (1972)
Recent Advances in Topological Manifolds.
Notes of Andrew Casson's 1971 Cambridge Part III course.
LATEX'ed from Andrew Ranicki's handwritten notes (1971).
Geometric Topology, Part I. Localization, periodicity and Galois symmetry
Dennis Sullivan's MIT notes (1970), K-Monograph 8, Springer (2005)
Whitehead groups of generalized free products
This is an important unpublished 1969 preprint of Friedhelm Waldhausen;
although the splitting of the Whitehead group claimed here is somewhat
wrong (the short exact sequence for Wh(A*_CB) does not split; the
`stable basis' on page 5.7 does not exist) it is a readable introduction to the
subsequently published papers in the Battelle 1972 Seattle proceedings,
and the monumental 1978 Annals paper "The algebraic K-theory of generalized
free products", which are certainly correct!
Lectures on the theorem of Browder and
Novikov and Siebenmann's thesis by M. Kervaire, Tata notes (1969)
Piecewise Linear Topology
The classic book by J.F.P.Hudson, originally published by Benjamin (1969)
Seminar notes on simply connected
surgery by Peter Orlik, Institute for Advanced Study (1968).
Proceedings of Conference on
Algebraic Topology, University of Illinois at Chicago Circle, 1968,
including memorial to Victor Gugenheim.
Le theoreme du h-cobordisme (Smale)
Notes by Jean Cerf and Andre Gramain (Ecole Normale Superieure, 1968).
Thanks to Shu Otsuka for the retyped version.
Le fibre tangent
Notes by Larry Siebenmann (Orsay, 1966)
The Relation of Cobordism to K-Theories,
by P.E.Conner and E.E.Floyd, Springer Lecture Notes 28 (1966)
Introduction to topology,
by E.C.Zeeman, notes (Warwick, 1966).
Thanks to Shu Otsuka for the retyped version.
Lectures on polyhedral topology by J.Stallings (Tata, 1967).
Turning a surface inside out by Anthony Phillips, (Scientific American, May 1966).
Everting a sphere Website.
The obstruction to finding a boundary for an open manifold of dimension
greater than five
Larry Siebenmann's thesis (Princeton, 1965).
Retyped LATEX version.
Lectures on the h-cobordism theorem
by J.Milnor, (Mathematical Notes 1, Princeton, 1965)
Seminar on Combinatorial Topology
by E.C.Zeeman. Chapters 1.-4. IHES (1963), 5.-8. Warwick(1966).
Notes of Warwick course (1966)
(by Rainer Vogt).
Proceedings of CIME, Urbino conference (1962).
J.Cerf Invariants des paires d'espaces.
Applications à la topologie differentielle.
A.Haefliger Varietes feuilletées.
M.Kervaire La methode de Pontryagin pour la classification des applications
sur une sphere.
S.Smale Stable manifolds for differential equations and diffeomorphisms.
John Henry Constantine Whitehead. 1904-1960
by M. H. A. Newman, Biographical Memoirs of Fellows of the Royal Society, Vol. 7 (Nov., 1961), pp. 349-363.
C.T.C.Wall's Part III course (Cambridge, 1960-1961).
Retyped by Shu Otsuka (2011).
Differentiable Manifolds Which Are Homotopy
Spheres by J. Milnor, mimeo notes (Princeton, 1959)
Higher inverse limits and homology theories
by Z. Yeh, (Ph.D. thesis, Princeton, 1959)
by J. Milnor, mimeo notes (Princeton, 1958).
Retyped version (2010)
by Shu Otsuka (with some additional material).
Lectures on Characteristic Classes
by J. Milnor, mimeo notes (Princeton, 1957).
Basis for the Milnor-Stasheff book Characteristic classes (Annals Study, 1976).
Proceedings of 1956 Algebraic Topology Symposium in Mexico.
The birth of the Borel conjecture (Extract of letter
from Borel to Serre, 2 May 1953)
Sur une partition en cellules associee a une
fonction sur une variete by Rene Thom, C.R. Acad. Sci. Paris 228,
Topologie Algebrique Paris, 1947.
Vorlesungen über Topologie I: Flächentopologie
by B. Kerekjarto (Springer 1923) :
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
Analisis situs combinatorio
by Hermann Weyl, Revista Matematica Hispano-Americana 5, 390--432 (1923)
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
topology a respectable field? (Mathematical Survey Lectures, Springer,
Boy's immersion of the real projective plane in 3-space.
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
metal model of Boy's immersion made at the Mercedes-Benz factory in Stuttgart.
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 is
isomorphic to the cyclic group of order 8.
of the Kervaire invariant by E.H.Brown (Annals of Mathematics 95,
Example 1.28 shows that the isomorphism is defined
by the -valued Kervaire invariant.
8 Boys bound Movie made by Tony Phillips,
with supplementary material.
The movie illustrates Boy's immersion of the projective plane in ,
which generates the cobordism group, and how to bound 8 copies of it.
Note that 4 copies bound the immersion of the torus in
with nontrivial -valued Kervaire invariant.
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's papers on topology. English translation (2009) by
which are published
by the American Mathematical Society.
Poincaré website (in French, 2017)
from A Treatise on Electricity and Magnetism by James Clerk Maxwell (OUP 1873).
An essentially topological account of Stokes' theorem, using the
first (cyclomatic) and second (periphractic) Betti numbers,
and Poincaré-Lefschetz duality for surfaces with boundary,
as described in
Electromagnetic Theory and Computation: A Topological Approach by P.W.Gross and P.R.Kotiuga (MSRI/CUP 2001).
See also Iron Rings, Doctor Honoris Causa
Raoul Bott, and a Hidden Hand by P.R.Kotiuga (2010)
On Hills and Dales by James Clerk Maxwell,
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 4th Series,
40(269):421--425, December 1870. An early contribution to Morse theory.
Der Census räumlicher Complexe
oder Verallgemeinerung des Euler'schen Satzes von der Polyedern,
by J.B. Listing, Abh. der Konigl. Ges. der Wiss. Göttingen 10,
On Contours and Slope Lines by
Arthur Cayley, Philosophical Magazine, Vol. XVIII (1859), 264--268.
An even earlier contribution to Morse theory.
Vorstudien zur Topologie
by J.B.Listing, Göttinger Studien 1, 811--875 (1847)