GAP (simpcomp) - References

Goto Chapter: Top 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Bib Ind
[Top of Book] [Contents] [Previous Chapter] [Next Chapter]

[MathJax off]

### References

[Ban65] Banchoff, T. F., Tightly embedded \(2\)-dimensional polyhedral manifolds, Amer. J. Math., 87 (1965), 462--472.

[Ban74] Banchoff, T. F., Tight polyhedral Klein bottles, projective planes, and M\"obius bands, Math. Ann., 207 (1974), 233--243.

[BBP+14] Burton, B. A., Budney, R., Pettersson, W. and others,, Regina: normal surface and 3-manifold topology software, Version 4.97 (1999--2014), {\tt http://\allowbreak regina.\allowbreak sourceforge.\allowbreak net/}.

[BD08] Bagchi, B. and Datta, B., Lower bound theorem for normal pseudomanifolds, Expo. Math., 26 (4) (2008), 327--351.

[BD11] Bagchi, B. and Datta, B., On Walkup's class \(\mathcal K(d)\) and a minimal triangulation of \((S^3 \dtimes S^1)^{\#3}\), Discrete Math., 311 (12) (2011), 989--995.

[BDS16] Bagchi, B., Datta, B. and Spreer, J., A characterization of tightly triangulated 3-manifolds (2016)
(Preprint, 6 pages, 2 figures), \texttt{arXiv:1601.00065 [math.GT]}.

[BDSS15] Burton, B. A., Datta, B., Singh, N. and Spreer, J., Separation index of graphs and stacked 2-spheres, J. Combin. Theory Ser. A, 136 (2015), 184--197.

[BK97] Banchoff, T. F. and K{\"u}hnel, W., Tight submanifolds, smooth and polyhedral, in Tight and taut submanifolds (Berkeley, CA, 1994), Cambridge Univ. Press, Math. Sci. Res. Inst. Publ., 32, Cambridge (1997), 51--118.

[BK08] Brehm, U. and K{\"u}hnel, W., Equivelar maps on the torus, European J. Combin., 29 (8) (2008), 1843--1861.

[BK12] Brehm, U. and K{\"u}hnel, W., Lattice triangulations of \(E^3\) and of the \(3\)-torus, {Israel J. Math.}, 189 (2012), 97--133.

[BL98] Breuer, T. and Linton, S., The GAP 4 type system: organising algebraic algorithms, in Proceedings of the 1998 international symposium on Symbolic and algebraic computation, ACM, ISSAC '98, New York, NY, USA (1998), 38--45.

[BL00] Bj{\"o}rner, A. and Lutz, F. H., Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincar\'e homology 3-sphere, Experiment. Math., 9 (2) (2000), 275--289.

[BL14a] Benedetti, B. and Lutz, F. H., Random discrete Morse theory and a new library of triangulations, Exp. Math., 23 (1) (2014), 66--94.

[BL14b] K. Adiprasito B. Benedetti, and Lutz, F. H., Random Discrete Morse Theory II and a Collapsible 5-Manifold Different from the 5-Ball. (2014), {\tt arXiv:1404.4239 [math.CO]}, 20 pages, 6 figures, 2 tables.

[BR08] Barakat, M. and Robertz, D., \tt homalg: a meta-package for homological algebra, J. Algebra Appl., 7 (3) (2008), 299--317.

[BS14] Burton, B. A. and Spreer, J., Combinatorial Seifert fibred spaces with transitive cyclic automorphism group (2014)
(26 pages, 10 figures. To appear in Israel Journal of Mathematics), \texttt{arXiv:1404.3005 [math.GT]}.

[CK01] Casella, M. and K{\"u}hnel, W., A triangulated \(K3\) surface with the minimum number of vertices, Topology, 40 (4) (2001), 753--772.

[Con09] Conder, M. D. E., Regular maps and hypermaps of Euler characteristic \(-1\) to \(-200\), J. Combin. Theory Ser. B, 99 (2) (2009), 455--459.

[Dat07] Datta, B., Minimal triangulations of manifolds, J. Indian Inst. Sci., 87 (4) (2007), 429--449.

[DHSW11] Dumas, J. -.G., Heckenbach, F., Saunders, B. D. and Welker, V., Simplicial Homology, v. 1.4.5 (2001--2011), {\url{http://www.cis.udel.edu/~dumas/Homology/}}.

[DKT08] Desbrun, M., Kanso, E. and Tong, Y., Discrete differential forms for computational modeling, in Discrete differential geometry, Birkh\"auser, Oberwolfach Semin., 38, Basel (2008), 287--324.

[Eff11a] Effenberger, F., Hamiltonian submanifolds of regular polytopes, Logos Verlag, Berlin (2011)
(Dissertation, University of Stuttgart, 2010).

[Eff11b] Effenberger, F., Stacked polytopes and tight triangulations of manifolds, Journal of Combinatorial Theory, Series A, 118 (6) (2011), 1843 - 1862.

[Eng09] Engstr{\"o}m, A., Discrete Morse functions from Fourier transforms, Experiment. Math., 18 (1) (2009), 45--53.

[For95] Forman, R., A discrete Morse theory for cell complexes, in Geometry, topology, \& physics, Int. Press, Cambridge, MA, Conf. Proc. Lecture Notes Geom. Topology, IV (1995), 112--125.

[Fro08] Frohmader, A., Face vectors of flag complexes, Israel J. Math., 164 (2008), 153--164.

[GJ00] Gawrilow, E. and Joswig, M., polymake: a framework for analyzing convex polytopes, in Polytopes---combinatorics and computation (Oberwolfach, 1997), Birkh{\"a}user, DMV Sem., 29, Basel (2000), 43--73.

[Gr\03] Gr{\"u}nbaum, B., Convex polytopes, Springer-Verlag, Second edition, Graduate Texts in Mathematics, 221, New York (2003), xvi+468 pages
(Prepared and with a preface by Volker Kaibel, Victor Klee and G{\"u}nter M.\ Ziegler).

[GS] Grayson, D. R. and Stillman, M. E., Macaulay2, a software system for research in algebraic geometry, Available at http://www.math.uiuc.edu/Macaulay2/.

[Hak61] Haken, W., Theorie der Normalfl\"achen, Acta Math., 105 (1961), 245--375.

[Hau00] Hauser, H., Resolution of singularities 1860--1999, in Resolution of singularities (Obergurgl, 1997), Birkh\"auser, Progr. Math., 181, Basel (2000), 5--36.

[Hir53] Hirzebruch, F. E. P., \"Uber vierdimensionale Riemannsche Fl\"achen mehrdeutiger analyti\-scher Funktionen von zwei komplexen Ver\"anderlichen, Math. Ann., 126 (1953), 1 -- 22.

[Hop51] Hopf, H., \"Uber komplex-analytische Mannigfaltigkeiten, Univ. Roma. Ist. Naz. Alta Mat. Rend. Mat. e Appl. (5), 10 (1951), 169--182.

[Hud69] Hudson, J. F. P., Piecewise linear topology, W. A. Benjamin, Inc., New York-Amsterdam, University of Chicago Lecture Notes prepared with the assistance of J. L. Shaneson and J. Lees (1969), ix+282 pages.

[Hup67] Huppert, B., Endliche Gruppen. I, Springer-Verlag, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Berlin (1967), xii+793 pages.

[KL99] K{\"u}hnel, W. and Lutz, F. H., A census of tight triangulations, Period. Math. Hungar., 39 (1-3) (1999), 161--183
({D}iscrete geometry and rigidity ({B}udapest, 1999)).

[KN12] Klee, S. and Novik, I., Centrally symmetric manifolds with few vertices, Adv. Math., 229 (1) (2012), 487--500.

[Kne29] Kneser, H., Geschlossene Fl\"achen in dreidimensionalen Mannigfaltigkeiten, Jahresbericht der deutschen Mathematiker-Vereinigung, 38 (1929), 248--260.

[KS77] Kirby, R. C. and Siebenmann, L. C., Foundational essays on topological manifolds, smoothings, and triangulations, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo (1977), vii+355 pages
(With notes by John Milnor and Michael Atiyah, Annals of Mathematics Studies, No. 88).

[K\t86] K{\"u}hnel, W., Higher dimensional analogues of Cs\'asz\'ar's torus, Results Math., 9 (1986), 95--106.

[K\t94] K{\"u}hnel, W., Manifolds in the skeletons of convex polytopes, tightness, and generalized Heawood inequalities, in Polytopes: abstract, convex and computational (Scarborough, ON, 1993), Kluwer Acad. Publ., NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 440, Dordrecht (1994), 241--247.

[K\t95] K{\"u}hnel, W., Tight polyhedral submanifolds and tight triangulations, Springer-Verlag, Lecture Notes in Mathematics, 1612, Berlin (1995), vi+122 pages.

[Kui84] Kuiper, N. H., Geometry in total absolute curvature theory, in Perspectives in mathematics, Birkh{\"a}user, Basel (1984), 377--392.

[Lut] Lutz, F. H., The Manifold Page, {\url{http://www.math.tu-berlin.de/diskregeom/stellar}}.

[Lut03] Lutz, F. H., Triangulated Manifolds with Few Vertices and Vertex-Transitive Group Actions, Ph.D. thesis, TU Berlin (2003).

[Lut05] Lutz, F. H., Triangulated Manifolds with Few Vertices: Combinatorial Manifolds (2005), {\tt arXiv:math/0506372v1 [math.CO]}, Preprint, 37 pages.

[MP14] McKay, B. D. and Piperno, A., Practical graph isomorphism, \II\ , Journal of Symbolic Computation , 60 (0) (2014), 94 - 112.

[Pac87] Pachner, U., Konstruktionsmethoden und das kombinatorische Hom\"oomorphieproblem f\"ur Triangulierungen kompakter semilinearer Mannigfaltigkeiten, Abh. Math. Sem. Uni. Hamburg, 57 (1987), 69--86.

[PS15] Paix{\~a}o, J. and Spreer, J., Random collapsibility and 3-sphere recognition (2015)
(Preprint, 18 pages, 6 figures), \texttt{arXiv:1509.07607 [math.GT]}.

[Rin74] Ringel, G., Map color theorem, Springer-Verlag, New York (1974), xii+191 pages
(Die Grundlehren der mathematischen Wissenschaften, Band 209).

[RS72] Rourke, C. P. and Sanderson, B. J., Introduction to piecewise-linear topology, Springer-Verlag, New York (1972), viii+123 pages
(Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69).

[R\t13] R\"{o}der, M., GAP package polymaking (2013), {\url{https://www.gap-system.org/Packages/polymaking.html}}.

[Sch94] Schulz, C., Polyhedral manifolds on polytopes, Rend. Circ. Mat. Palermo (2) Suppl. (35) (1994), 291--298
(First International Conference on Stochastic Geometry, Convex Bodies and Empirical Measures (Palermo, 1993)).

[SK11] Spreer, J. and K{\"u}hnel, W., Combinatorial properties of the K3 surface: Simplicial blowups and slicings, Experiment. Math., 20 (2) (2011), 201--216.

[Soi12] Soicher, L. H., GRAPE - GRaph Algorithms using PErmutation groups (2012)
({Version 4.6.1}), {\url{https://www.gap-system.org/Packages/grape.html}}.

[Spa56] Spanier, E. H., The homology of Kummer manifolds, Proc. AMS, 7 (1956), 155--160.

[Spa99] Sparla, E., A new lower bound theorem for combinatorial \(2k\)-manifolds, Graphs Combin., 15 (1) (1999), 109--125.

[Spr11a] Spreer, J., Blowups, slicings and permutation groups in combinatorial topology, Ph.D. thesis, Logos Verlag Berlin, University of Stuttgart (2011), 251 pages
(Ph.D. thesis).

[Spr11b] Spreer, J., Normal surfaces as combinatorial slicings, Discrete Math., 311 (14) (2011), 1295--1309
({\tt doi:10.1016/j.disc.2011.03.013}).

[Spr12] Spreer, J., Partitioning the triangles of the cross polytope into surfaces, {Beitr. Algebra Geom. / Contributions to Algebra and Geometry}, 53 (2) (2012), 473--486.

[Spr14] Spreer, J., Combinatorial 3-manifolds with transitive cyclic symmetry, Discrete Comput. Geom., 51 (2) (2014), 394--426.

[Wee99] Weeks, J., SnapPea (Software for hyperbolic \(3\)-manifolds) (1999)
(\url{http://www.geometrygames.org/SnapPea/}).

[Wil96] Wilson, D. B., Generating random spanning trees more quickly than the cover time, in Proceedings of the Twenty-eighth Annual ACM Symposium on the Theory of Computing (Philadelphia, PA, 1996), ACM, New York (1996), 296--303.

[Zie95] Ziegler, G. M., Lectures on polytopes, Springer-Verlag, Graduate Texts in Mathematics, 152, New York (1995), x+370 pages.

[Top of Book] [Contents] [Previous Chapter] [Next Chapter]
Goto Chapter: Top 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Bib Ind

generated by GAPDoc2HTML