Izbrana poglavja iz topologije

Pogojev za vključitev v delo ni.

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, 2nd revised and extended ed., Berlin : W. de Gruyter, 2003.
2. R. E. Gompf, A. I. Stipsicz: 4-manifolds and Kirby calculus, Providence : American Mathematical Society, cop. 1999.
3. P. Hilton, G. Mislin, J. Roitberg: Localization of nilpotent groups and spaces, Amsterdam : North-Holland ; New York : American Elsevier, 1975.
4. D. Husemoller: Fibre bundles, 3rd ed. - New York : Springer, cop. 1994.
5. H. B. Lawson, M.-L. Michelsohn: Spin geometry, Princeton (New Jersey) : Princeton University Press, 1989.
6. J. McCleary: A user's guide to spectral sequences, 2nd ed. - New York : Cambridge University Press, cop. 2001.
7. J. Milnor, Morse theory, Princeton (New Jersey) : Princeton Univ. Press, 1963.
8. C. P. Rourke, B. J. Sanderson: Introduction to piecewise-linear topology, Berlin : Springer, 1972, 1982.
9. E. H. Spanier, Algebraic topology, New York : Springer, cop. 1966.
10. G. W. Whitehead: Elements of homotopy theory, New York : Springer, cop. 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]