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Acknowledgements

The style of the publication list mimics the output of bibtex2html with BibTEX style amsplain.

The XHTML+MATHML format of preprints are a compactified form of what was generated by TEX4HT from LATEX sources. I highly recommend this software as it supports many LATEX constructs, packages and output formats. Its author, Eitan Gurari, is friendly, responsive and active.

Notes on formats

I do not have the sources for some items. These are available in fewer formats with possibly lower quality.

Pdf:
Generally high quality, optimized for printing but also suitable for online viewing (bookmarks, hyperlinks).
XHTML+MATHML:
experimental, readable by browsers supporting MATHML (tested only with browsers based on Mozilla), but maybe of low quality. As of 2007 January, the documents are valid.

Publications

  1. Gábor Braun and Rüdiger Göbel, Automorphism groups of nilpotent groups, Arch. Math. (Basel) 80 (2003) 5 464–474 MR 1 995 625 Zbl 1031.20032 doi:10.1007/s00013-003-0802-4

    Abstract. The stabiliser group of an automorphism group of a class 2 nilpotent group is the normal subgroup consisting of elements acting trivially on the centre of the group and on the factor gof the group by the centre. We construct torsion-free class 2 nilpotent groups whose automorphism group is the semidirect product of the stabiliser group and an arbitrary group.

    2000 Mathematics Subject Classification: Primary:20F18; Secondary:18B15, 20F28

    Keywords: class 2 nilpotent group; automorphism group.

  2. Gábor Braun and Rüdiger Göbel, Outer automorphisms of locally finite p-groups, J. Algebra 264 (2003) 1 55–67 MR 1 980 685 Zbl 1060.20031

    Abstract. Every group has a semidirect product with a locally finite p-group such that the result has an arbitrary outer automorphism group.

    2000 Mathematics Subject Classification: Primary:20F28; Secondary:20F29, 20F50

    Keywords: outer automorphism group; locally finite p-group; Black Box.

  3. Gábor Braun and Rüdiger Göbel, E-algebras whose torsion part is not cyclic, Proc. Amer. Math. Soc. 133 (2005) 8 2251–2258 (electronic) MR 2138867 Zbl 1069.16036

    Abstract. A generalized E-algebra is an algebra isomorphic to its own algebra of module endomorphisms. We give examples of such algebras over a Dedekind domain whose torsion part is not cyclic. It is based on earlier construction of torsion-free E-algebras.

    2000 Mathematics Subject Classification: Primary:16S50; Secondary:16Dxx

    Keywords: mixed E-rings; Dedekind domain.

  4. Gábor Braun, Outer automorphism groups, Ph.D. thesis, Universität Duisburg-Essen, 2003

    Abstract. If the continuum hypothesis holds then there exists a locally finite p-group of cardinality the successor of countably infinite with trivial centre and outer automorphism group. Without any additional set theoretic hypotheses, every group is an outer automorphism group of arbitrary many locally finite p-groups.

    2000 Mathematics Subject Classification: Primary:20F28; Secondary:20E22, 20F19, 20F50

    Keywords: locally finite p-group; outer automorphism group; Black Box; Continuum Hypothesis.

  5. Gábor Braun, A proof of Higgins's conjecture, Bull. Austral. Math. Soc. 70 (2004) 2 207–212 MR 2094288 Zbl 1080.20021 arXiv:math.GR/0312139

    Abstract. Higgins conjectured a generalization of two theorems on decomposition of subgroups of free product of groups: Kuroš Theorem and his own generalization of Grušhko's Theorem. We prove this conjecture by improving Higgins's proof of these theorems using groupoids and covers.

    2000 Mathematics Subject Classification: Primary:20E06; Secondary:

    Keywords: free product of groups; free product of goupoids; Kuroš's theorem; Higgins's theorem; Gruško's theorem.

  6. Gábor Braun, Characterization of matrix types of ultramatricial algebras, New York J. Math. 11 (2005) 21–33 Zbl 1089.20035

    Abstract. The matrix type of an algebra is an equivalence relation on natural numbers. Two numbers n and m are equivalent if the ring of n × n matrices is isomorphic to the ring of m × m matrices. We prove that matrix types of ultramatricial algebras over any field is in bijection with subgroups of the multiplicative group of positive rational numbers

    2000 Mathematics Subject Classification: Primary:20K30, 16S50; Secondary:06F20, 19A19

    Keywords: matrix type of a ring; dimension group; ultramtaricial algebra; automorphism group of a dimension group.

  7. Gábor Braun, The cobordism class of the multiple points of immersions, Algebraic & Geometric Topology (2008) 8 581–601 doi:10.2140/agt.2008.8.581 arXiv:math.AT/0409574

    Abstract. Let us take an arbitrary immersion with even codimension. We derive an explicit formula for the characteristic classes of its multiple point manifolds. The main trick is solving a recursion on cohomology classes using power series.

    2000 Mathematics Subject Classification: Primary:57R20, 57R42; Secondary:16W60, 57R75

    Keywords: multiple-point manifold; immersion; cobordism class; generating function.

  8. Andreas Blass and Gábor Braun, Random Orders and Gambler's Ruin, Electronic Journal of Combinatorics 12 (2005) 1 R23 Zbl 1075.05004

    Abstract. Solving a conjecture of Droste and Kuske, we compute the probability that a gambler will play at least a given number of rounds with a given initial wealth in the Gambler's Ruin game with a biased coin. We present several approaches to the problem.

    2000 Mathematics Subject Classification: Primary:05A15; Secondary:05A19, 60C05

    Keywords: gambler's ruin; random linear order.

  9. Gábor Braun and Gábor Lippner, Characteristic numbers of multiple-point manifolds, Bull. London Math. Soc. (2006) 38 667–678 doi:10.1112/S0024609306018571

    Abstract. We derive a recursion for the cohomology classes of multiple point manifolds of an arbitrary immersion with even codimension.

    2000 Mathematics Subject Classification: Primary:57R42; Secondary:57R20, 57R75

    Keywords: multiple-point manifold; characteristic number.

  10. Gábor Braun and András Némethi, Invariants of Newton non-degenerate surface singularities, Compositio Mathematica (2007) 143 1003–1036 MR 2339837 Zbl pre05177033 arXiv:math.AG/0609093

    Abstract. We consider Newton non-degenerate, isolated surface singularities whose link is a rational homology sphere. We provide an algorithm to compute the Newton boundary of such a singularity from its resolution graph.

    2000 Mathematics Subject Classification: Primary:14J17, 14Q10; Secondary:52B20

    Keywords: hypersurface singularities, links of singularities, resolution graphs, Newton boundary, Newton polyhedrons.

    Remark. Publisher provided doi:10.1112/S0010437X07002941 does not resolve, so it is not linked.

  11. Gábor Braun and András Némethi, Surgery formulas for Seiberg–Witten invariants of negative definite plumbed 3-manifolds, Journal für die reine und angewandte Mathematik 2010 638 189–208 doi:10.1515/CRELLE.2010.007 arXiv:0704.3145

    Abstract. We provide a surgery formula for the Seiberg–Witten invariants of negative definite plumbed rational homology 3-spheres. The surgery is deleting an arbitrary vertex of the plumbing graph. The formula is additive in nature: the Seiberg–Witten invariant for a c spinorial structure is the sum of correction terms plus the Seiberg–Witten invariants for the restricted c spinorial structure of the manifolds plumbed using the components of the deleted graph. This formula was conjectured by the second author as an analogue of Okuma's additivity formula for splice-quotient singularities. As a by-product, this proves the Seiberg–Witten invariant conjecture for splice-quotient singularities.

    2000 Mathematics Subject Classification: Primary:57R57, 57M27; Secondary:32S05, 32S25, 32S45, 32C35

    Keywords: isolated surface singularity, plumbed 3-manifold, surgery formula for Seiberg–Witten invariants, rational homology sphere, splice-quotient singularity, Seiberg–Witten invariant conjecture.

  12. Gábor Braun, Geometry of splice-quotient singularities, 2008 submitted to Transactions of the American Mathematical Society arXiv:0812.4403

    Abstract. We obtain a new important basic result on splice-quotient singularities in an elegant combinatorial-geometric way: every level of the divisorial filtration of the ring of functions is generated by monomials of the defining coordinate functions. The elegant way is the language of of line bundles based on Okuma's description of the function ring of the universal abelian cover. As an easy application, we obtain a new proof of the End Curve Theorem of Neumann and Wahl.

    2000 Mathematics Subject Classification: Primary:14F05, 14J25; Secondary:14C17, 32S05, 32S50

    Keywords: splice-quotient singularity, End Curve Theorem, divisorial filtration.

  13. Rüdiger Göbel and Gábor Braun, Splitting kernels into small summands, Israel Journal of Mathematics (2009) accepted

    Abstract. Let λ be a regular cardinal. An epimorphism between abelian groups is λ-pure if it is projective with respect to abelian groups of size less than λ. We show that every cotorsion group have λ-pure projective dimension greater than 1 if and only if λ is smaller than the torsion-free part of the group. (For larger λ, the groups are λ-pure projective.) This is related to a (hard) problem of Neeman in module theory about writing modules as factors of direct sums of small modules.

    2000 Mathematics Subject Classification: Primary:20K25; Secondary:20K21, 20K99

    Keywords: Direct sums, direct products, mixed abelian groups, cotorsion groups.

  14. Gábor Braun and Lutz Strüngmann, Breaking up finite automata presentable torsion-free abelian groups, International Journal of Algebra (2010) accepted

    Abstract. We show that every torsion-free group representable by a finite automaton is an extension of a finite-rank free group by a direct sum of finitely many Prüfer groups. This builds on a large extent on Tsankov's proof that the group of rational numbers is not representable by a finite automaton.

    2000 Mathematics Subject Classification: Primary:20K15; Secondary:03D05, 20K35, 68R15

    Keywords: FA-presentable abelian groups, automatic structures, additive combinatorics.

  15. Gábor Braun and Sebastian Pokutta, Rank of random half-integral polytopes (extended abstract), Electronic Notes in Discrete Mathematics (2010) 36 415–422 doi:10.1016/j.endm.2010.05.053

    Abstract. We will show that random half-integral polytopes contain certain sets with high probability, the sets of k-tuples with entries in {0, 1/2 , 1}, and exactly one entry equal to 1/2. We precisely determine the threshold number k for which the phase transition occurs. Using these random polytopes we show that establishing integer-infeasibility takes Ω(log n/ log log n) rounds of (almost) any cutting-plane procedure with high probability whenever the number of vertices is θ(3^n). As a corollary, a relationship between the number of vertices and the rank of the polytope with respect to (almost) any cutting-plane procedure follows.

    2000 Mathematics Subject Classification: Primary:60C05; Secondary:90C10, 90C27, 90C57

    Keywords: random 0-1 polytopes; cutting-plane procedure; integer infeasibility.