Not actively under construction. While I collect the will to put something
useful here, please do try a small bridge-building
game or a variaton of box puzzles and mail me with any feedback, comments,
suggestions, bugs, whatever you want. A known problem is that they currently
only work under IE, I have fixed the bridge-building game to function on
FireFox, will do the same with the other one sometime.
Minden esetre: pont-összekötő,egy
légy szíves, próbáld ki és írd meg nekem a
JScript test, not working.
Actually, I'll try to do something with this mess.
Allen Hatcher's page.
Okay, how can I not start by this one? The guy's written darn good books
about algebraic topology and he put them up for everybody to use for
free! I say, that deserves at least a visit to his homepage (and
chances are, you will be staying there for quite a while).
2014/2015 tavaszi félév algebrai
és differenciáltopológia beadhatók
2014/2015 őszi félév
Self-promotion is allegedly an important pastime. So eventually a list of my
papers should be linked here as well. If you're still reading and are
actually interested, here's a short summary:
If you want a copy of either of those papers which don't have a link
attached to them, or just want to talk about maths (any maths, not only
analysis) please e-mail me.
- ELTE TTK
maths MSci theses have mine, check under year 2004. It's about some
silly messing with level sets (point preimages) of a somewhat weird class of
mappings. There are some really nice results about them (e.g. this one), and thankfully there
are also relatively accessible (if practically unusable) problems that help
young people construct their theses.
- Cobordisms of fold maps and
maps with prescribed number of cusps, contribution to the work of
András Szűcs and Tobias Ekholm. This has been published in Kyushu Journal of
Mathematics 61/2 (2007), pp. 395—414, and it's about observing how
do the cobordism groups of
manifolds or mappings change if we restrict ourselves solely to "nice" maps
having only regular and fold points.
- Cobordisms of fold maps of 2k+2-manifolds into
R3k+2, Geometry and topology of caustics, Banach Center
Publications vol. 82 (2008), pp. 209—213 (proceedings of the Caustics
'06 symposium). Same thing, in
another dimension, when the calculations are not quite as simple and easy
since the objects to avoid are whole curves of cusps and not just discrete
- Calculation of the avoiding ideal for
Σ1,1, Algebraic Topology — Old and New, Banach Center
Publications vol.85 (2009), 307—313. Another path for attacking the same problem,
and in the complex setting it actually works all the time. In the real
setting, well, fold maps is the most complicated case where it still works
that I'm aware of.
- Bordism groups of fold maps (joint with András
Szűcs), Acta Mathematica Hungarica 126/4 (2010), pp. 334—351. The
concept of classifying spaces is what makes singular cobordisms conceptually
very nice, one can translate singular cobordisms to homotopies in the
classifying space. The one tiny problem with this is that classifying spaces
are hard to construct, and after construction we need to calculate
their homotopic properties, which is typically hard in itself (just think
about the homotopy groups of spheres, and spheres are not complicated to
construct). So here we do some calculations in the smallest classifying
space that has not been understood by the great figures of the past, who did
consider the classifying space for immersions. We can only do homological
calculations, but at least those do work and yield some geometric results.
- Fibration of classifying spaces in the cobordism theory of
singular maps, Proceedings of the Steklov Institute of Mathematics vol.
267 (2009), pp. 270—277. I am fond of the result of this paper,
because it is a geometric proof of a very useful fact that previously only
had a quite contrived proof. The statement is that when one constructs
classifying spaces for a set of singularities and then adds exactly one
other monosingularity, then there is a fibration involving the two
classifying spaces and the space that classifies the "new"
singular locus as a decorated immersion. The use of this lies in the fact
that it allows calculations with homotopy groups, which fibrations handle
nicely, of classifying spaces, whose standard construction is a pile of
gluings and thus not conductive to homotopic calculations at all.
Additionally, making the proof simpler also allows extending it to settings
where the original proof didn't work, so good things all around.
- Calculation of the obstruction ideals of Morin maps,
Periodica Mathematica Hungarica 63/1 (2011), pp. 89—100. Here we get a
set of relations among the characteristic classes of the virtual normal
bundle of a map with only some Morin singularities, that is, relatively
easily computable obstructions to the existence of a deformation of a given
map without sufficiently ugly singularities. This set is actually maximal if
we consider not only honest maps, but also fiber-preserving bundle maps. The
drawback is that we only look at cohomology with modulo 2 coefficients, and
there's the slight aesthetic problem of these obstructions being mostly due
to the exclusion of non-Morin singularities. I don't know how to enhance the
calculation to address maps that only avoid swallowtails
(Σ1,1,1), for example.
- On bordism
and cobordism groups of Morin maps (joint with Endre Szabó and
Journal of Singularities, vol. 1 (2010), pp. 134—145. A pretty
technical paper, we get lucky calculating the rational homology of the
classifying space of Morin maps, and consequently get results for rational
homotopy groups and the rational cobordism groups.
- Proof of a conjecture of V. Nikiforov, Combinatorica 31/6
(2011), pp. 739—754. Nothing to do with topology, although the
inspiration did come from Morse theory and I would have liked to push that
analogy further than I finally managed to. I heard a friend of mine talk
about the conjecture, and under the influence of thinking about dense graph
limits I had the idea to work directly on the optimal limit of the question,
and there to test optimality locally under reparametrisations. It's slightly
annoying that in the end, one still needs to sift through a (luckily
small-dimensional) family of candidates, and this causes the method to
essentially fail in all the generalisations that I've tried so far.
- Relations among characteristic
classes and existence of singular maps (joint with Boldizsár
AMS 364 (2012), pp. 3751—3779. Here we look at negative
codimensional maps (so the dimension of the source manifold is larger than
the dimension of the target), which are Boldizsár's speciality, not
mine. The main idea is to get calculable cohomological obstructions by first
eliminating the singularities of the fold or Morin map — by blowing up
the source along the singular set and perturbing the result —
and then tracking the restrictions obtained from now having a nicer map to
work with. There's a surprising amount of concrete calculations that can be
done that way, some may be doable in positive codimensional setting as well.
- Large 2-coloured matchings in
3-coloured complete hypergraphs, submitted to Electronic Journal of Combinatorics.
This is another paper far from my main competence, I attended a
combinatorics workshop, encountered the problem and it stuck in my head. The
proof I found is not very enlightening, but I harbour a faint hope that one day
similar problems may be attacked with the dense graph limit approach. That
would be awesome.
- Singularities and stable
homotopy groups of spheres I (joint with Csaba Nagy and András
Szűcs) and Singularities and
stable homotopy groups of spheres II (joint with András
Szűcs) apply the classifying space machinery in a case when the
classifying space does not become mind-bogglingly complicated. For that, one
needs singularities with few automorphisms, so we start with codimension 1
Morin maps, whose symmetry group is C2×C2,
require them to be cooriented (reducing the symmetry group to a single
C2), and finally asking for a trivialization of the kernel
bundle, eliminating homotopically nontrivial symmetries altogether. From
another point of view, these are exactly the projections of immersions into
one higher dimension, and this allows us to identify the gluing maps of the
classifying space (which describe what the less complicated singular points
do around more complicated singular points) with maps in a spectral sequence
associated to the filtration of the complex projective space CP∞
by the CPn, and those latter maps have been studied quite a lot.
Project Euler. Not really maths, more
compsci, but as long as I don't drag up something fun, it'll do. Maybe I
will be able to get my hands on anatomical images with the parabolic curves
drawn, like in the Hilbert-Cohn Vossen book, those would be fun, right?
use Excel to avoid using real languages when I'm lazy and the task at hand
Travel Cost Calculator for Pardus:
DISCONTINUED xls version: Cost calculator (xls)
Update: I've worked on this some more, the current state of affairs is
here. Press "Load map data" first, and "Process
map data" after the appropriate textbox gets populated. Aliases are not
maintained, but that's
something for active players anyway; feel free to roll your own list and use
My proof-of-concept entry for 4E6.
Sandbox for internal use