Papers
All my papers on the Arxiv (but exclude the Atiyah lectures!)
Cocycles on the mapping class group and symplectic groups (with
Dave Benson, Caterina Campagnolo
and Carmen Rovi)
e-print arxiv:1710.04851
(2018)
Cohomology of symplectic groups and Meyer's signature theorems (with
Dave Benson, Caterina Campagnolo
and Carmen Rovi)
e-print arxiv:1710.04851
(2017) To appear in Algebraic and Geometric Topology
Solid angles and Seifert hypersurfaces (with
Maciej Borodzik and Supreedee Dangskul)
e-print arxiv:1706.06405 Submitted for publication (2017)
Signatures in algebra, topology and dynamics
(with Etienne Ghys).
Arxiv 1512.092582.
Ensaios matematicos, Volume 30, 1-173 (2016)
Mathematical Reviews, Zentralblatt review.
Morse theory for manifolds with boundary (with
Maciej Borodzik and
Andras Nemethi),
e-print arxiv:1207.3066 (2012).
Algebraic and Geometric Topology 16, 971-1023 (2016)
Commentary on the Kervaire-Milnor correspondence 1958-1961 (with Claude Weber),
Bull. Amer. Math. Soc. 52, 603-609 (2015). Included in the October
2015 issue of the Bulletin of the American Mathematical Society devoted to the topologist John Milnor.
On the semicontinuity of the mod 2 spectrum of hypersurface singularities (with
Maciej Borodzik and
Andras Nemethi),
e-print arxiv:1207.0798, Published in
Journal of Algebraic Geometry 24, 379-398 (2015).
Codimension 2 embeddings, algebraic surgery and Seifert forms (with
Maciej Borodzik and
Andras Nemethi),
e-print arxiv:1211.5964 (2012).
Under revision
On the algebraic L-theory of Δ-sets (with Michael Weiss)
e-print
math.0701833.
Pure and Applied Mathematics Quarterly (issue dedicated to
F. Thomas Farrell and Lowell E. Jones) Vol. 8, 423--449 (2012)
Commentary on
On the parallelizability of the spheres by R. Bott and J. Milnor and
On the nonexistence of elements of Hopf invariant one by J. F. Adams,
Bull. Amer. Math. Soc. 48, 509-511 (2011)
Algebraic K-theory over the infinite
dihedral group: an algebraic approach, (with Jim Davis and
Qayum Khan)
e-print math.0803.1639
Algebraic and Geometric Topology 11, 2391--2436 (2011)
The geometric Hopf invariant and double
points (with Michael Crabb).
e-print
math.1002.2907
J. of Fixed Point Theory and Applications 7,
The Steve Smale Festschrift, 325--350 (2010)
Book review: The Novikov conjecture, geometry
and algebra, by M.Kreck and W.Lück, Bull. L.M.S. 42, 181--183 (2010)
On the construction
and topological invariance of the Pontryagin classes (with Michael Weiss).
e-print
math.0901.0819
Geometriae Dedicata (issue dedicated to Bruce Williams) 148, 309--343 (2010)
A composition formula for manifold
structures e-print math.0608705.
Pure and Applied Mathematics Quarterly, Vol. 5 (2)
(Hirzebruch 80th birthday issue), 701--727 (2009)
The signature of a fibre bundle is
multiplicative mod 4 (with Ian Hambleton and
Andrew Korzeniewski)
Geometry & Topology 11, 251-314 (2007)
e-print AT.0502353.
Companion paper to Absolute
Whitehead torsion (by Andrew Korzeniewski)
Geometry & Topology 11, 215-249 (2007)
e-print AT.0502349.
Blanchfield and Seifert algebra in
high-dimensional boundary link theory I. Algebraic K-theory (with
Des Sheiham)
Geometry and
Topology 10, 1761--1853 (2006)
e-print AT.0508405.
The quadratic form E_8 and exotic homology
manifolds (with Washington
Mio), e-print
AT.0403261
Proceedings
2003 Oberwolfach meeting on exotic homology manifolds , Geometry
and Topology Monograph 9, 33--66 (2006).
Controlled L-theory (with Masayuki Yamasaki) e-print AT.0402217
in Proceedings
2003 Oberwolfach meeting on exotic homology manifolds , Geometry
and Topology Monograph 9, 105--153 (2006)
Algebraic and combinatorial codimension 1
transversality
e-print AT.0308111
Geometry and Topology Monographs, Vol. 7
(2004), Proceedings of the Casson Fest, Paper no. 6, pages 145--180.
Generalized Arf invariants in algebraic
L-theory (with Markus Banagl)
e-print AT.0304362
Advances in Mathematics 199, 542-668 (2006)
On the calculation of UNil (with Frank
Connolly) e-print
AT.0304016, Advances in Mathematics 195, 205--258 (2005).
Noncommutative localization in topology e-print AT.0303046
Proc. 2002 ICMS Edinburgh meeting on Noncommutative Localization
in Algebra and Topology, LMS
Lecture Notes Series 330 Cambridge University Press, 81--102
(2006).
Blanchfield and Seifert algebra in
high-dimensional knot theory e-print GT.0212187
Moscow Mathematical Journal 3, 1333-1367 (2003).
Rigidity and glueing for Morse and Novikov
complexes (with Octav
Cornea) e-print
AT.0107221
Journal of the European Mathematical Society 5,
343--394 (2003)
Representations of algebras as universal
localizations (with Amnon Neeman and Aidan Schofield) e-print AT.0205034
Mathematical Proceedings of the Cambridge Philosophical Society
136, 105--117 (2003)
Noncommutative localization in chain complexes I. Algebraic K- and
L-theory. e-print RA.0109118 (2001) (with Amnon Neeman).
The work in this e-print was subsequently divided into 3 papers:
Noncommutative localisation in algebraic
K-theory. I. Geometry and Topology 8 (2004), 1385--1425 (with Amnon Neeman).
Noncommutative localisation in algebraic
K-theory. II. Advances in Mathematics 213 (2007) 785--819
(by Amnon Neeman).
Noncommutative localization in algebraic
L-theory. Advances in Mathematics 220 (2009) 894--912.
Circle valued Morse theory and Novikov
homology
School
on High-dimensional Manifold Topology, 543--569, ICTP Trieste
(2002). e-print
AT.0111317
The structure set of an arbitrary space,
the algebraic surgery exact sequence and the total surgery
obstruction
School
on High-dimensional Manifold Topology, 519--538, ICTP Trieste
(2002). e-print
AT.0111316
Foundations of algebraic surgery
School on High-dimensional Manifold Topology, 495--514, ICTP Trieste (2002). e-print AT.0111315
Controlled surgery with trivial local
fundamental groups (with Erik Pedersen and Frank Quinn) e-print AT.0111269
Proceedings 2001 ICTP School on High-dimensional Manifold Topology,
World Scientific, 421--426 (2003)
The algebraic construction of the Novikov
complex of a circle-valued Morse function
Mathematische
Annalen 322, 745--785 (2002). The e-print AT.9903090 version has diagrams!
Algebraic Poincare cobordism
in
"Topology, geometry and algebra: interactions and new directions",
Proc. 1999 Milgram Conference, Stanford,
Contemporary Mathematics
279, A.M.S., 213--255 (2001), e-print AT.0008228
An introduction to algebraic surgery
in Surveys on Surgery Theory, Vol. 2, Annals of Mathematics Studies
149, 81--163, Princeton (2001), e-print AT.0008070
A survey of Wall's finiteness obstruction
(with Steve Ferry)
in
Surveys on Surgery Theory, Vol. 2, Annals of Mathematics Studies 149,
63--80, Princeton (2001), e-print AT.0008070
The Whitehead group of the Novikov ring
(with
Andrei Pajitnov) K-theory 21, 325--365 (2000) e-print
AT.0012031
C.T.C. Wall's contributions to the topology
of manifolds (with Sylvain Cappell and Jonathan Rosenberg)
+
Wall's publication list up to 1999, Surveys on Surgery Theory, Vol. 1,
Annals of Mathematics Studies 145, 3--15, 17--24 , Princeton
(2000)
Homology manifold bordism (with Heather
Johnston) Trans. A.M.S. 352, 5093--5137 (2000), e-print
AT.9909130
The Morse-Novikov theory of circle-valued
functions and noncommutative localization (with Michael Farber)
Proc.
1998 Moscow Conference for S.P.Novikov's 60th Birthday, Proc. Steklov
Inst. 225, 381--388 (1999), e-print DG.9812122
Singularities, double points, controlled
topology and chain duality
Documenta Mathematica 4, 1--59 (1999)
Applications of chain
duality to local invariants of Poincar\'e complexes and maps of
manifolds, with homological obstructions answering:
(1) Is a
polyhedron with Poincar\'e duality a homology manifold?
(2) Does a
degree 1 PL map of polyhedral homology manifolds have acyclic point
inverses?
The paper may be regarded as a combinatorial
introduction to controlled topology and surgery theory.
The Maslov
index and the Wall signature non-additivity invariant
Unpublished notes (1997)
Notes on Reidemeister torsion
Unpublished notes (1997)
Controlled L-theory (Preliminary
announcement) (with Masayuki Yamasaki)
The extension to L-theory of Controlled
K-theory. Proceedings of Sakado
Conference on Surgery and Geometric Topology
Science Bulletin
of Josai University 2, 119--136 (1997)
On the Hauptvermutung
Introductory
survey published in the Hauptvermutung
Book K-theory Monograph 1, Kluwer (1996)
Book review: The topological classification of
stratified spaces, by S.Weinberger, Mathematical Review MR1308714 (96b:57024) (1996)
Bordism of automorphisms of manifolds from
the algebraic L-theory point of view
Proc. 1994 Princeton
conference in honour of W.Browder,
Ann. of Maths. Study 138,
314--327, Princeton University Press (1995)
On the Novikov conjecture
Survey
published in Novikov conjectures, Index theorems and Rigidity
LMS Lecture Notes 226, 272--337, Cambridge University Press (1995)
A History and Survey of the Novikov
Conjecture (with S.Ferry and J.Rosenberg)
Published in Novikov
conjectures, Index theorems and Rigidity
LMS Lecture Notes
226, 7--66, Cambridge University
Press (1995)
Controlled K-theory (with Masayuki Yamasaki)
A
self-contained account of the controlled algebraic K_0- and K_1-groups,
including the applications to proofs of Chapman's result on the
topological invariance of Whitehead torsion, and West's result on the
homotopy finiteness of compact ANR's.
Topology and Its Applications
61, 1--59 (1995)
Finite domination and Novikov rings
The main result is that an infinite cyclic cover of a finite CW complex
is finitely dominated if and only if the homology groups with
coefficients in the Novikov rings are acyclic.
Topology 34,
619--632 (1995)
A message from Dan Grayson
Zentralblatt review by Hans Munkholm
Symmetric and quadratic complexes with
geometric control (with Masayuki Yamasaki)
Proc. of Topology and Geometry Research Center, Kyungpook National
University, Vol. 3, 139--152 (1993)
Surgery obstructions of fibre bundles
(with
Wolfgang Lueck)
The generalization to surgery obstructions of
the formulae of Atiyah, Lusztig and Meyer for the non-multiplicativity
of the signature in a fibre bundle.
Journal of Pure and Applied
Algebra 81, 139--189 (1992)
The Maslov index and the Wall signature non-additivity invariant
Unpublished paper (1991)
The L-theory of Laurent extensions and genus 0
function fields (with Jim Milgram)
J. f. reine und angew.
Math. 406, 121--166 (1990)
Chain complexes and assembly (with
Michael Weiss)
Math. Z. 204, 157--185 (1990)
Additive L-theory
K-theory 3,
163--195 (1989)
Chain homotopy projections (with
Wolfgang Lueck)
J. Algebra 120, 361--391 (1989)
Jordan normal form projections (with
K.Y.Lam and L.Smith)
Archiv der Mathematik 50, 113--117 (1988)
Surgery transfer (with
Wolfgang Lueck)
Proceedings of 1987 Goettingen Topology
conference
Springer Lecture Notes 1361, 167--246 (1988)
Round L-theory (with Ian Hambleton and
Larry Taylor)
J. Pure and Applied Algebra 47, 131--154 (1987)
The L-theory of twisted quadratic
extensions
Can. J. Math. 39, 345--364 (1987)
Intrinsic transversality structures
(with Norman Levitt)
Pacific J. Math. 129, 85--144 (1987)
The algebraic theory of torsion II.
Products
K-theory 1, 115--170 (1987)
Semi-invariants in surgery (with Jim
Davis)
K-theory 1, 83--109 (1987)
Algebraic and geometric splittings of the K-
and L-groups of polynomial extensions
Proc. 1985 Poznan
Topology Conf., Springer Lecture Notes 1217, 321--363 (1986)
The algebraic theory of torsion I.
Proceedings of 1983 Rutgers Topology conference
Springer Lecture
Notes 1126, 199--237 (1985)
Some product formulae for nonsimply
connected surgery problems (with Jim Milgram)
Trans. A.M.S.
297, 383--413 (1985)
The algebraic theory of finiteness
obstruction
Math. Scand. 57, 105--126 (1985)
Book review: K-theory of forms,
by A.Bak, Bull. A.M.S. 7, 279--280 (1982)
The projective class group transfer induced
by an S1-bundle (with Hans
Munkholm)
Proc. 1981 London, Ontario Topology Conf., CMS Conf.
Proc. 2, 461--484 (1982)
Projective surgery theory (with Erik Pedersen)
Topology 19, 239--254 (1980)
The algebraic theory of surgery I.
Proc. London Math. Soc. (3) 40, 87--192 (1980)
The algebraic theory of surgery II.
Proc. London Math. Soc. (3) 40, 193--283 (1980)
The total surgery obstruction
Proceedings of 1978 Arhus Topology conference
Springer Lecture
Notes 763, 275--316 (1979)
Localization in quadratic L-theory
Proceedings of 1978 Waterloo Topology conference
Springer Lecture
Notes 741, 102--157 (1979)
The surgery obstruction of a disjoint
union
J. London Math. Soc. (2) 20, 559--566 (1979)
The algebraic theory of surgery (unpublished notes,
Princeton, 1978)
An algebraic formulation of surgery (unpublished
research fellowship dissertation, Trinity College, Cambridge, 1972)
Most of the material in the dissertation and notes was
subsequently published in The algebraic theory
of surgery I. and II.,
Exact sequences in the algebraic theory of
surgery, The total surgery obstruction and
Algebraic L-theory and topological
manifolds.
On the algebraic L-theory of semisimple
rings
J. Algebra 50, 242--243 (1978)
A semi-local combinatorial formula for the
signature of a 4k-manifold (with Dennis Sullivan)
J.
Differential Geometry 11, 23--29 (1976)
Algebraic L-theory, IV: Polynomial
extensions
Comm. Math. Helv. 49, 137--167 (1974)
Algebraic L-theory, III: Twisted Laurent
extensions
Proc. 1972 Battelle Seattle Algebraic K-theory
Conf., Vol. III., Springer Lecture Notes 343, 412--463 (1973)
Algebraic L-theory, II: Laurent
extensions
Proc. London Math. Soc. (3) 27, 126--158 (1973)
Algebraic L-theory, I: Foundations
Proc.
London Math. Soc. (3) 27, 101--125 (1973)