Bjørn Ian Dundas

Scientific Interests

If you don't feel that this list tells you very much, you may consult my pages "Space" exploration: there are groovier spaces than the universe, Goodwillie calculus or The sphere spectrum (all 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.

Classes

Books

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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

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Differential Topology

An introduction used for the course on manifolds at NTNU the last ten years. 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).

The version as of Jan. 10, 2013 (the one that was most recent at the beginning of the spring semester 2013), Jan. 23, 2013 (minor modification fixing up some typos). If you need older versions, you can find some here. The most recent version can always be found as http://www.math.uib.no/~dundas/dt/dtcurrent.pdf. Please report any known issues with the current or metastable edition asap.
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 on the notes, please contact me. (old versions: (2007, A4, 2002, US letter size, 2002))

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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

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Gummistrikk-geometri - fra matematikkens 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. It can be ordered from Vitensenteret by sending a mail to postkasse at viten.ntnu.no.

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Papers

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. Degreewise K-theory. 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.

Baas, Nils A.; Dundas, Bjørn Ian; Richter, Birgit and Rognes, John Ring completion of rig categories. J. reine angew. Math. (Crelle's Journal), Online March 23, 2012

Preprints.

Integral excision for K-theory, Dundas and Kittang, To appear in HHA

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 10th-11th 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

Current students

Former students at UiB.

List of old projects at NTNU.

RCN projects headed by the Bergen Topology group

Topology, (RCN project 2008-2012)

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