Bjørn Ian Dundas

Scientific Interests
Preprints and notes
Former (NTNU, UiB) and current students,
Suggestions for master's projects
Email is the best way of getting hold of me: 2017/18 I have a sabbatical and 2018/19 I am coorganizing the program in natural sciences at CAS/The Norwegian Academy for Sciences and Letters in Oslo.
my face
4A4d Realfagbygget, Allegaten 41, 4 etg
E-mail address:
dundas at
(47) 5558 2827
(47) 5558 9672
Snail mail address:
Department of Mathematics
University of Bergen
Postboks 7800
5020 Bergen
A. Solheia 7
N-5251 Søreidgrend
home:   (47) 5512 0614,
mobile: (47) 976 22 576

Scientific Interests

(Algebraic) K-theory, (motivic or stable) homotopy theory, (topological) cyclic homology, and so on.

If you don't feel that this list tells you very much, you may consult my pages Topologi på roterommet, "Romforskning", Goodwillie calculus or The sphere spectrum (some in Norwegian, they are really my notes for some popular lectures) where I try to give a brief and inadequate idea of various aspects of topology. You may also benefit from the "survey articles for the general public" posted on Hopf and the Wikipedia topology, algebraic topology and algebraic K-theory entries.

For what it's worth, my published papers have been classified according to the AMS Mathematics Subject Classification under 11, 13, 14, 16, 18, 19, 55, 57 and 81, with 19 by far the most frequent.


(UiB changes platforms ever so often, so many links will be dead)
Course Semester
MAT243 Manifolds spring 2017
MAT211 Real analysis fall 2016
MAT243 Manifolds spring 2016
MAT244 Algebraic Topology fall 2015
MAT344 Cohomology fall 2015
MAT342 Differential Geometry fall 2015
MAT243 Manifolds spring 2015
MAT229 Algebraic Geometry I fall 2014
MAT343 Calculus/Applied topology fall 2013
MAT229 Algebraic Geometry I spring 2013
MAT211 Real analysis fall 2012
MAT343 Simplicial methods fall 2012
MAT243 Manifolds spring 2012
MAT211 Real analysis fall 2011
Course Semester
MAT121 Linear Algebra spring 2010
MAT343 Simplicial methods spring 2010
MAT341 Algebraic Topology fall 2009
MAT121 Linear Algebra spring 2009
MAT342 Differential forms fall 2008
MAT225 Number theory fall 2008
MAT243 Manifolds spring 2008
MAT224 Commutative algebra fall 2007
MAT243 Manifolds spring 2007
MAT221 Discrete mathematics fall 2006
MAT224 Commutative algebra spring 2006
MAT111 Grunnkurs i matematikk I fall 2005
Algebraic topology spring 2005
MAT111 Grunnkurs i matematikk I fall 2004
MAT242 Topologi fall 2004
my face


The Local structure of algebraic K-theory

Bjørn Ian Dundas, Tom G. Goodwillie and Randy McCarthy

Algebra and Applications, Springer, 2012, XV, 435 p. 5 illus. ISBN 978-1-4471-4392-5

Springer has allowed me to keep a copy of the text on my home page. The pdf-file you find here is the next to last version before the galley proof (and so has some very minor differences from the printed edition). To get the correct numberings for exact reference, please refer to the printed version.

Differential Topology

differential topologyAn introduction to smooth manifolds. Since it has been available on the internet it has been used at several universitites, either as main text or as supplementary reading (and kindly mentioned in the Mathematical Intelligencer).

NEW: The text will undergo a last revision in August 2017, so if you have any comments this will be most welcome. If all goes well, in the future it will be possible to get hard copies from the Cambridge University Press (they promised to make it good-looking), but I have been allowed to keep the current version publicly available at this site.

The most recent version can be found as

If you need older versions, you can find some here.

If you plan to use these notes as course material or otherwise have them tested on a wider audience, or if you just have some comments, please contact me. The irony in that I open with claiming that "the earth is (fairly) flat" at the same time as the revisions have been undertaken in an "inspiring environment" (combined with climbing the local mountains and fishing in the occasionally rough seas of Northern Norway) has not escaped me; it is not to be considered a typo.


Motivic Homotopy Theory

Dundas, B.I., Levine, M., Østvær, P.A., Röndigs, O., Voevodsky,
Unversitext/Springer 2007. X 226p, Jahren (ed). ISBN 978-3-540-45897-5

"This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject."

«Gummistrikkgeometri» - fra matematikkens magiske skattekiste

joint with Nils Kristian Rossing. Vitensenteret i Trondheim, juli 2003, ISBN 82-92088-19-9. A popular exposition of some topological features (in Norwegian) written for teachers and other interested laymen. Contains some typos. It can be ordered from Vitensenteret by sending a mail to postkasse at


Dundas, Bjørn Ian. Fibrations and homology sphere bordism. Math. Scand. 72 (1993), no. 1, 20--28. 57Q20 (55R05)

Dundas, Bjørn Ian; McCarthy, Randy. Stable $K$-theory and topological Hochschild homology. Ann. of Math. (2) 140 (1994), no. 3, 685--701. 19D55 (18G60 19D06)

Dundas, Bjørn Ian; McCarthy, Randy. Topological Hochschild homology of ring functors and exact categories. J. Pure Appl. Algebra 109 (1996), no. 3, 231--294. 19D55 (16E40 18G30 18G60)

Dundas, Bjørn Ian. Relative K-theory and topological cyclic homology. Acta Math. 179 (1997), no. 2, 223--242. 19D55

Dundas, Bjørn Ian. K-theory theorems in topological cyclic homology. J. Pure Appl. Algebra 129 (1998), no. 1, 23--33. 19-XX (16Exx)

Dundas, Bjørn Ian. Continuity of K-theory: an example in equal characteristics. Proc. Amer. Math. Soc. 126 (1998), no. 5, 1287--1291. 11Sxx (13Jxx 19D45 19D55)

Dundas, Bjørn Ian. On K-Theory of Simplicial Rings and Degreewise Constructions. K-theory 18 (1999), 77--92. 19D06, 18G30, 19D25, 16N20

Dundas, Bjørn Ian. The Cyclotomic trace for symmetric monoidal categories. in "Geometry and Topology: Aarhus (1998)", 121--143, Contemp. Math., 258, Amer. Math. Soc., Providence, RI, 2000. 19D23 (18D20 19D55 55P43)

Dundas, Bjørn Ian. Localization of V-categories. Theory Appl. Cat. 8 (2001), pp. 284-312. 18D20 (18G55)

Dundas, Bjørn Ian; Röndigs, Oliver and Østvær, Paul Arne, Enriched functors and stable homotopy theory. Documenta Mathematica, Vol. 8 (2003), 409-488. 55P42 (18D20 55P91 55U35)

Dundas, Bjørn Ian; Röndigs, Oliver and Østvær, Paul Arne, Motivic Functors, Documenta Mathematica, Vol. 8 (2003), 489-525. 55P42 (14F42)

Baas, Nils A.; Dundas, Bjørn Ian and Rognes, John Two-vector bundles and forms of elliptic cohomology. In Topology, Geometry and Quantum Field Theory, LMS Lecture note series 308, Cambridge University Press. Ed. Ulrike Tillmann (2004), p. 18--45. 55N34 (18D05 57T30)

Dundas, Bjørn Ian, The cyclotomic trace for S-algebras. J. London Math. Soc. (2) 70 (2004), no. 3, 659--677. 19D23 (18D20 19D55 55P43)

Dundas, Bjørn Ian, Prerequisites in algebraic topology in "Motivic Homotopy Theory" Unversitext/Springer 2007, Dundas/Levine/Østvær/Röndigs/Voevodsky. Jahren (ed).

Dundas, Bjørn Ian and Kittang, Harald Excision for K-theory of connective ring spectra, Homology, Homotopy and Applications, vol. 10(1), 2008, pp. 29 - 39

Ausoni, Christian; Dundas, Bjørn Ian; Rognes, John Divisibility of the Dirac magnetic monopole as a two-vector bundle over the three-sphere. Doc. Math. 13 (2008), 795--801.

Brun, Morten; Carlsson, Gunnar and Dundas, Bjørn Ian Covering homology. Adv. Math. 225 (2010), 3166-3213.

Carlsson, Gunnar; Douglas, Cristopher L. and Dundas, Bjørn Ian Higher topological cyclic homology and the Segal conjecture for tori. Adv. Math. 226 (2011), 1823-1874.

Baas, Nils A.; Dundas, Bjørn Ian; Richter, Birgit and Rognes, John Stable bundles over rig categories. J. Topology 4 (2011), 623-640.

Dundas, Bjørn Ian and Kittang, Harald Integral excision for K-theory, Homology, Homotopy and Applications, vol. 15(1), (2013), 1 - 25.

Baas, Nils A.; Dundas, Bjørn Ian; Richter, Birgit and Rognes, John Ring completion of rig categories. J. Reine Angew. Math. 674 (2013), 43 - 80

Dundas, Bjørn Ian and Morrow, Matthew, Finite generation and continuity of topological Hochschild and cyclic homology, Ann. Sci. Ec. Norm. Super. (4) 50 (2017), no. 1, 201 - 238.

Dundas, Bjørn Ian and Skau, Christian, Interview with Abel Laureate Yves Meyer, Eur. Math. Soc. Newsl. No. 105 (2017) 14-22.


On higher topological Hochschild homology of rings of integers, Dundas, Lindenstrauss and Richter. To appear in Math. Research Letters.

Equivariant Structure on Smash Powers, Brun, Dundas, Stolz, 2016

Towards an understanding of ramified extensions of structured ring spectra, Dundas, Lindenstrauss, Richter. 2016. Submitted

Higher Hochschild homology is not a stable invariant, Dundas, Tenti. 2016. Submitted

Cubical and cosimplicial descent, Dundas, Rognes, 2017. Submitted

Various unofficial notes and talks.

Norwegian topology symposia, and some other conferences I have (co)organized or given lecture series in.

The schedule for the mini symposium on ring spectra, K-Theory and trace invariants in Oslo, March 26th-28th 1998.
The schedule for the mini symposium in algebraic K-theory and homotopy theory in Trondhjem, November 5th-6th 1998.
The schedule for the mini symposium on algebraic K-Theory and topology in Oslo, May 25th-26th 1999.
The schedule for the mini symposium on topology in Trondhjem, November 16th-17th 1999.
The workshop on mathematics education for engineering students in Trondhjem, May 29-30, 2000.
The schedule for the mini symposium on topology in Trondhjem, November 9th-10th 2000.
The ski and mathematics meeting in Oppdal January 4th-7th 2001.
The summer school Motivic homotopy theory Sophus Lie Conference Center, Nordfjordeid, Norway, 12.-16. August 2002
The ski and mathematics meeting at Rondablikk January 9th-12th 2003.
The schedule for the topology meeting in Oslo, May 15th-16th 2003.
The schedule for the topology symposium in Trondhjem, November 25th-26th 2004.
Homological methods in algebra and topology, session at the 24th Nordic and 1st Franco-Nordic Congress of Mathematicians, Reykjavik, Iceland, January 6th - 9th 2005
The schedule for the topology symposium in Oslo, June 2nd-3rd 2005.
The Nordic Conference in Topology in Trondhjem, November 24th-25th 2006.
The topology symposium in Bergen, June 11th-12th 2007.
The Abel symposium in Oslo, August 5th-10th 2007.
Spring symposium, May 21st-23rd 2008 at Thorbjørnrud near Oslo
Nordic topology meeting, November 27 - 28 2008, Trondheim
The algebraic topology session at the 25th Nordic and 1st British-Nordic congress of Mathematicians, 2009.
The Nordic topology symposium in Bergen, June 10-11 2010.
The Algebra, Topology and Fjords! Summer School, Nordfjordeid, Norway June 3rd - 11th 2011.
The Advances in K-theory West coast algebraic topology summer school 2012, Stanford University, July 16-21 2012
The Topology symposium in Bergen, June 13-14 2013.
The Invariants of Structured Ring Spectra European Talbot Workshop 2015, 28 June - 4 July, 2015 Klosters, Switzerland
The Algebraic Topology - Summer School, Lisbon, July 24 - 28, 2017.

Current students

Kristian Alfsvåg (PhD, 2019)
Anders Husebø (PhD, 2018)
Stefano Piceghello (PhD, 2019)

Former students at UiB.

List of old projects at NTNU.


Homotopy Type Theory and Univalent Foundations (2018-2019 at CAS/the Norwegian Academy of Science and Letters in Oslo, PI Marc Bezem, BID)

Computational aspects of Univalence (RCN FRIPRO 2016-2019, PI Marc Bezem (Dept. of Computer Science, UiB) and BID)

Topology, (RCN project 2008-2012, PI BID)

TiN, (RCN project "Topology in Norway", 2004-2007, PI BID)

Bjørn Ian Dundas
Last modified: Last modified: Thurs Dec 22 13:48:12 CET 2016