Tibor Macko

Address:  Mathematical Institute

Slovak Academy of Sciences

Stefanikova 49

814 73 Bratislava


Email: macko (at) mat (dot) savba (dot) sk

Book project:

·         Diarmuid Crowley, Wolfgang Lueck, Tibor Macko : Surgery Book

This is a book project under construction. The chapters 1-9 are already in a reasonable shape. The subsequent chapters are very preliminary. At the moment the material is to be used at own risk. Comments are welcome per email to any of us!


·         Diarmuid Crowley and Tibor Macko:

On the cardinality of the manifold set, arXiv:1708.02089

Survey about topology of high-dimensional manifolds (in Slovak):

Topológia vysoko-rozmerných variet

Published papers:

·         Tibor Macko:

The block structure spaces of real projective spaces and orthogonal calculus of functors

Transactions of the American Mathematical Society, 359 (2007), no. 1, 349-383. arXiv:0404.5198

·         Joachim Grunewald, John Klein, and Tibor Macko:

Operations on A-theoretic nil-terms

Journal of Topology, Volume 1, Number 2, April 2008, 317-341. arXiv:0702.5580

·         Tibor Macko and Michael Weiss:

The block structure spaces of real projective spaces and orthogonal calculus of functors II

Forum Mathematicum 21 (2009), no. 6, 1091--1136 arXiv:0703.5303

·         Tibor Macko and Christian Wegner:

On fake lens spaces with the fundamental group of order a power of 2

Algebraic and Geometric Topology 9 (2009), no. 3, 1837—1883 arXiv:0805.0965

·         Diarmuid Crowley and Tibor Macko:

The additivity of the rho-invariant and periodicity in topological surgery

Algebraic and Geometric Topology 11 (2011), 1915–1959. arXiv:1002.1917

·         Tibor Macko and Christian Wegner:

On fake lens spaces

Forum Math. 23 (2011), no. 5, 1053–1091, arXiv:0810.1196

·         Philipp Kühl, Tibor Macko and Adam Mole:

The total surgery obstruction revisited

Münster J. Math. 6 (2013), 181–269, arXiv:1104.5092

·         Tibor Macko:

Fake lens spaces, Bulletin of the Manifold Atlas, 2013

·         Spiros Adams-Florou and Tibor Macko:

L-homology on ball complexes and products

To appear in Homology, Homotopy and Applications, arXiv:1611.04114



·         Diferenciálna Topológia, FMFI UK

Past teaching:

WS 2014/15

·         Bachelorthemen: Cliffordalgebren, Signatur


SS 2014

·         Bachelorbegleitseminar

·         Algebraic Topology II


WS 2013/14:

·         Signature theorem, S4D4, Organisational meeting 16.07.2013 at 10:15 in N0.003

(with Stefan Schwede)

·         Tutorials for Algebraic Topology I, V4D1, (with Christian Wegner)


SS 2013:

·         Characteristic classes, S2D2/S4D2, Organisational meeting 31.01.2013, 12:10-13:00, Room 2.008

(with Wolfgang Lück)

·         Übungen zu Topologie II, V3D2, (with Wolfgang Lück)


WS 2012/13:

·         Cohomology of groups, S4D2, Mi 10-12, Raum 1.007 (with Carl-Friedrich Bödigheimer)

·         Übungen zu Topologie I, V3D1, (with Wolfgang Lück)


SS 2012:

·         Coxeter Gruppen, S1G1, Mo 14-16, Raum 1.007 (with Martin Langer)

·         Charakteristische Klassen, S2D2, Do 10-12, Raum 0.003 (with Carl-Friedrich Bödigheimer)


SS 2012 Bachelorarbeitthemen:

·         Linsenräume


WS 2011/12:

·         The Steenrod Algebra, WS 2011/12, Tue 14-16, Room 0.006 (with Steffen Sagave)

·         Topologische K-Theorie, WS 2011/12, Do 8-10, Raum 0.007 (with Carl-Friedrich Bödigheimer)

SS 2011:

·         Charakteristische Klassen, SS 2011, Bonn, Dienstag, 14:15 - 16:00, Raum 1.007 (with Christian Wegner)

·         Probleme der euklidischen Geometrie, SS 2011, Bonn, Mo 14 (c.t.) - 16 MATH / N 0.007 (with Martin Langer)

WS 2009/10 (Münster):

·         Was ist … seminar?, WS 2009/10, Mon 16:00-18:00, SR 7 (with Arthur Bartels)

·         Der Index-Satz von Atiyah-Singer Seminar, WS 2009/10, Die 14:00-16:00, SR 5 (with Roman Sauer)

SS 2009 (Münster):

·         Reading seminar on algebraic surgery, SS 2009, Mon 16:00-18:00, SR 7 (with Arthur Bartels)

SS 2008 (Münster):

·         Introduction to surgery theory, lecture, SS2008, Tue 10:00-12:00 , SR 5


Research Seminars:

·         Stable parametrized h-cobordism theorem, SS 2011, Bonn, Th 14 (c.t.) - 17, every two weeks, Lipschitz Saal

(with Steffen Sagave and Wolfgang Steimle)

·         Mapping surgery to analysis, Münster, May 2010

(with Ján Špakula, Philipp Kühl and Wolfgang Steimle)



·         Oberwolfach workshop Surgery theory: organized together with Diarmuid Crowley and Andrew Ranicki, 2012

·         Summer school Topology of high-dimensional manifolds: organized together with Diarmuid Crowley and Wolfgang Lueck, 2014



Slides of talks:

·         Automorphisms of manifolds and algebraic theory of surgery, NRW Topology Meeting, Düsseldorf, 24.11.2007, pdf

·         On fake lens spaces, Oberseminar Topologie, Bonn, 6.11.2007, pdf

·         On fake lens spaces, Oberseminar Topologie, Münster, 27.10.2008, pdf

·         The total surgery obstruction III, Oberseminar Topologie, Münster, 22.06.2009,pdf

·         Algebraic L-theory, GK summer school, THDM, Bonn, August 2013, L-Theory-I.pdf, L-Theory-II.pdf


Research interests:

·         automorphisms of manifolds

·         surgery theory

·         algebraic K-theory

·         calculus of functors


·         Web page of Andrew Ranicki (surgery theory)

·         Web page of Allen Hatcher (algebraic topology)

·         Manifold Atlas

·         Fachbereich Mathematik Universität Münster

·         Dept of Maths, University of Aberdeen