Izbrana poglavja iz topologije

Izbrane bodo nekatere standardne podiplomske teme iz topologije, ki vključujejo splošno homotopsko teorijo, teorijo ovir, teorijo svežnjev in karakterističnih razredov, K-teorijo, teorijo Liejevih grupoidov, teorijo spektralnih zaporedij, Morsovo teorijo, teorijo vozlov itd. Izbira je odvisna od interesov in raziskovalne usmeritve študentov.

[1] G. Burde, H. Zieschang, Knots, de Gruyter Studies in Mathematics 5, Walter de Gruyter & Co., Berlin, 2003.
[2] R. E. Gompf, A. I. Stipsicz, 4-manifolds and Kirby calculus, Graduate Studies in Mathematics 20, AMS, Providence, 1999.
[3] P. Hilton, G. Mislin, J. Roitberg, Localization of nilpotent groups and spaces , Elsevier, Amsterdam 1975.
[4] D. Husemoller, Fibre bundles, Springer, New York, 1994.[5] H. B. Lawson, M. L. Michelsohn, Spin geometry, Princeton Mathematical Series 38, Princeton University Press, Princeton, 1989.
[6] J. McCleary, A user’s guide to spectral sequences , Cambridge University Press, Cambridge, 2001.
[7] J. Milnor, Morse theory, Annals of Mathematics Studies 51, Princeton University Press, Princeton, 1963.
[8] C. P. Rourke, B. J. Sanderson, Introduction to piecewise-linear topology, Springer Study Edition, Springer-Verlag, Berlin-New York, 1982.[9] E. Spanier, Algebraic topology, Springer, New York - Heidelberg - Berlin, 1966.
[10] G. W. Whitehead, Elements of homotopy theory, Springer, New York - Heidelberg - Berlin, 1978.

Namen predmeta je seznaniti študente z nekaterimi pomembnimi temami topologije.

Znanje in razumevanje predstavljenih konceptov.
Sposobnost uporabe pridobljenega znanja in spretnosti.

Predavanja, konzultacije, reševanje problemov

Pisni izpit (domače naloge), ustni izpit
(ocene: 5 (negativno), 6-10 (pozitivno), ob upoštevanju Statuta UL)

MOERDIJK, Ieke, MRČUN, Janez. Introduction to foliations and Lie groupoids, (Cambridge studies in advanced mathematics, 91). Cambridge, UK: Cambridge University Press, 2003. IX, 173 str., ilustr. ISBN 0-521-83197-0. [COBISS-SI-ID 12683097]
KALIŠNIK, Jure, MRČUN, Janez. A Cartier-Gabriel-Kostant structure theorem for Hopf algebroids. Advances in mathematics, ISSN 0001-8708, 2013, vol. 232, iss. 1, str. 295-310. [COBISS-SI-ID 16432473]
JELENC, Blaž, MRČUN, Janez. Homotopy sequence of a topological groupoid with a basegroup and an obstruction to presentability of proper regular Lie groupoids. ArXiv.org, 13 str. [COBISS-SI-ID 16400729]
FRANC, Aleksandra, PAVEŠIĆ, Petar. Spaces with high topological complexity. Proceedings. Section A, Mathematics, ISSN 0308-2105, 2014, vol. 144, iss. 4, str. 761-773. [COBISS-SI-ID 17096025]
PAVEŠIĆ, Petar. Fibrations between mapping spaces. Topology and its Applications, ISSN 0166-8641. [Print ed.], 2014, vol. 178, str. 276-287. [COBISS-SI-ID 17141337]
PAVEŠIĆ, Petar. Induced liftings, exchange rings and semi-perfect algebras. Journal of Pure and Applied Algebra, ISSN 0022-4049. [Print ed.], 2010, vol. 214, iss 11, str. 1901-1906. [COBISS-SI-ID 15627865]
REPOVŠ, Dušan. A two-parameter control for contractive-like multivalued mappings. V: 2010 International Conference on Topology and its Applications, June 26-30, 2010, Nafpaktos, Greece. 2010 International Conference on Topology and its Applications, (Topology and its applications, ISSN 0166-8641, Vol. 159, iss. 7). Amsterdam [etc.]: Elsevier, 2012, str. 1899-1905. [COBISS-SI-ID 16224857]
GARITY, Dennis, REPOVŠ, Dušan. Homogeneity groups of ends of open 3-manifolds. Pacific journal of mathematics, ISSN 0030-8730, 2014, vol. 269, no. 1, str. 99-112. [COBISS-SI-ID 17071961]
HEGENBARTH, Friedrich, REPOVŠ, Dušan. Controlled homotopy equivalences and structure sets of manifolds. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2014, vol. 142, no. 11, str. 3987-3999. [COBISS-SI-ID 17080665]
SMREKAR, Jaka. Turning a self-map into a self-fibration. Topology and its Applications, ISSN 0166-8641. [Print ed.], 2014, vol. 167, str. 76-79. [COBISS-SI-ID 16943705]
SMREKAR, Jaka. Homotopy type of space of maps into a K(G,n). Homology, homotopy, and applications, ISSN 1532-0073, 2013, vol. 15, no. 1, str. 137-149. [COBISS-SI-ID 16643929]
SMREKAR, Jaka. Homotopy type of mapping spaces and existence of geometric exponents. Forum mathematicum, ISSN 0933-7741, 2010, vol. 22, no. 3, str. 433-456. [COBISS-SI-ID 15638105]
RUBERMAN, Daniel, STRLE, Sašo. Concordance properties of parallel links. Indiana University mathematics journal, ISSN 0022-2518, 2013, vol. 62, no. 3, str. 799-814. [COBISS-SI-ID 16946265]
OWENS, Brendan, STRLE, Sašo. Dehn surgeries and negative-definite four-manifolds. Selecta mathematica. New series, ISSN 1022-1824, 2012, vol. 18, iss. 4, str. 839-854. [COBISS-SI-ID 16808025]
GRIGSBY, J. Elisenda, RUBERMAN, Daniel, STRLE, Sašo. Knot concordance and Heegaard Floer homology invariants in branched covers. Geometry & topology, ISSN 1364-0380, 2008, vol. 12, iss. 4, str. 2249-2275. [COBISS-SI-ID 14892121]