Nicolau Corção Saldanha

Publications

This is a list of my mathematical writings, whether actually published or just made public as some sort of preprint. Anything that has been published is indicated with reference. You may download TeX sources, postscript files and pdf files. If you prefer, you may view the papers as png files. Some publications (but not all) are also available in html format. Files are compressed with gzip and some browsers will uncompress them automatically but others will not; some will uncompress the file but not remove the .gz extention and thus confuse the user or other programs. If you cannot print or display the files as you get them, you may need to decompress them manually with gunzip.

Please consider anything you get here as an informal preprint obtained at personal request. Thus, you will find preliminary versions of some papers and partial copies of others (e.g., without the figures). The ``official'' version is what you see published on paper.

Please write to nicolaumat.puc-rio.br if you have any difficulties downloading documents.

Topology

Homotopy type of spaces of curves with constrained curvature on flat surfaces

With Pedro Zühlke.

Also at http://www.arxiv.org/abs/1410.8590.

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Components of spaces of curves with constrained curvature on flat surfaces

With Pedro Zühlke. To appear in Pacific Journal of Mathematics.

Also at http://www.arxiv.org/abs/1312.1675.

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On The Components of Spaces of Curves on the 2-Sphere with Geodesic Curvature in a Prescribed Interval

With Pedro Zühlke. International Journal of Mathematics, Vol. 24, No. 14 (2013) 1350101 (78 pages).
doi:10.1142/S0129167X13501012

Also at http://www.arxiv.org/abs/1304.2629.

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The homotopy type of spaces of locally convex curves in the sphere

Geometry and Topology 19 (2015) 1155-1203; DOI: 10.2140/gt.2015.19.1155.
Also at http://www.arxiv.org/abs/1207.4221.

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The homotopy and cohomology of spaces of locally convex curves in the sphere --- I

Also at http://www.arxiv.org/abs/0905.2111.

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The homotopy and cohomology of spaces of locally convex curves in the sphere --- II

Also at http://www.arxiv.org/abs/0905.2116.

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Spaces of locally convex curves in S^n and combinatorics of the group B^+_{n+1}

With Boris Shapiro. Journal of Singularities, 4, 1-22, 2012. Also at http://www.arxiv.org/abs/math/0703803.

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Stability of compact actions of the Heisenberg group

With Tania M. Begazo. Also at http://www.arxiv.org/abs/math.GT/0412501.

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Homotopy and cohomology of spaces of locally convex curves in the sphere

Also at http://www.arxiv.org/abs/math.GT/0407410.

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Nilpotent pseudogroups of functions on an interval

With Tania M. Begazo. Bull Braz Math Soc, New Series 36(1), 25-38 (2005). Also at http://www.arxiv.org/abs/math.DS/0404157.

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Stability of compact actions of Rn of codimension one

Comment. Math. Helvetici, 69, 431-446 (1994).

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Actions of Rn over Tn-fibrations

Preprint.

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An introduction to geometric topology: Geometric Structures on 2 and 3-Manifolds

Contemporary Mathematics, vol. 161 (Differential Topology, Foliations, and Group Actions), 1994.

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Differential equations

The geometry of the critical set of nonlinear periodic Sturm-Liouville operators

With Dan Burghelea and Carlos Tomei. J. Differential Equations 246, 3380-3397 (2009). doi:10.1016/j.jde.2008.10.021

Also at http://arxiv.org/abs/0707.1256

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The topology of the monodromy map of a second order ODE

With Dan Burghelea and Carlos Tomei. J. Differential Equations 227, 581-597 (2006).

Also at http://www.arxiv.org/abs/math.CA/0507120

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The topology of critical sets of some ordinary differential operators

With Carlos Tomei. Progress in Nonlinear Differential Equations and Their Applications, Vol. 66, 491-504 (2005).

Also at http://www.arxiv.org/abs/math.FA/0501071

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Results on infinite dimensional topology and applications to the structure of the critical set of nonlinear Sturm-Liouville operators

With Dan Burghelea and Carlos Tomei. J. Differential Equations 188, 569-590 (2003).

Also at http://www.arxiv.org/abs/math.FA/0107197

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Morin singularities and global geometry in a class of ordinary differential operators

With Iaci Malta and Carlos Tomei. Topological Methods in Non-linear analysis, 10:137-169 (1997).

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The version above incorporates corrections to the original version of the paper. See below the errata as published in TMNA.

With Carlos Tomei. Topological Methods in Non-linear analysis, 32:411-414 (2008).

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The paper above received a Featured Review from Math Reviews.

Regular level sets of averages of Nemytskii operators are contractible

With Iaci Malta and Carlos Tomei. Journal of Functional Analysis, 143, no. 2, 461-469 (1997).

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Linear algebra and spectral theory

Dynamics of the symmetric eigenvalue problem with shift strategies

With Ricardo S. Leite and Carlos Tomei. International Mathematics Research Notices 2012; doi: 10.1093/imrn/rns186

Also at http://arxiv.org/abs/1108.6030.

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The Asymptotics of Wilkinson's Iteration: Loss of Cubic Convergence

With Ricardo S. Leite and Carlos Tomei. Foundations of Computational Mathematics, 10 (1), 15-36, 2010. doi:10.1007/s10208-009-9047-3

Also at http://www.arxiv.org/abs/0807.0415.

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An atlas for tridiagonal isospectral manifolds

With Ricardo S. Leite and Carlos Tomei. Linear Algebra and Applications, vol. 429, 387-402 (2008). doi:10.1016/j.laa.2008.03.001

Also at http://www.arxiv.org/abs/math.SP/0608558.

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Reconstruction of tridiagonal matrices from spectral data

With Ricardo S. Leite and Carlos Tomei. Also at http://www.arxiv.org/abs/math.NA/0508099.

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The asymptotics of Wilkinson's shift iteration

With Ricardo S. Leite and Carlos Tomei. Also at http://www.arxiv.org/abs/math.NA/0412493.

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The Accumulated Distribution of Quadratic Forms on the Sphere

With Carlos Tomei. Linear Algebra and Applications, vol. 245, 335-351 (1996).

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Tilings

Domino tilings of three-dimensional regions: flips, trits and twists

With Pedro Milet. At http://arxiv.org/abs/1410.7693.

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Polytopes

Spectra of semi-regular polytopes

With Carlos Tomei. Boletim da Sociedade Brasileira de Matemática, vol. 29, n. 1, 25-51 (1998).

Also at http://www.arxiv.org/abs/math.CO/9712252

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Spectra of regular polytopes

With Carlos Tomei. Discrete Comput. Geom. 7:403-414 (1992).

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Functions in the plane

Functions from R2 to R2: a study in nonlinearity

With Carlos Tomei.

Also at http://www.arxiv.org/abs/math.NA/0209097

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The numerical inversion of functions from the plane to the plane

With Iaci Malta and Carlos Tomei. Mathematics of Computation 65, no. 216, 1531-1552 (1996).

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Critical sets of proper Whitney functions in the plane

With Iaci Malta and Carlos Tomei. Matemática Contemporânea, SBM, vol. 13, 10th Brazilian Topology Meeting, 181-228 (1997).

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On the problem of solving F(x) = y in the plane

With Iaci Malta and Carlos Tomei. Matemática Contemporânea, SBM, vol. 3, 89-107 (1992).

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Editor

Foliations, Geometry, and Topology: Paul Schweitzer Festschrift

Editors: Nicolau C. Saldanha, Lawrence Conlon, Rémi Langevin, Takashi Tsuboi, Pawel Walczak;
AMS, 2009, 232 pp., ISBN-10: 0-8218-4628-0, ISBN-13: 978-0-8218-4628-5, CONM/498.

Books

Teoria dos números: um passeio com primos e outros números familiares pelo mundo inteiro

In portuguese. With Fabio Brochero Martinez, Carlos G. Moreira and Eduardo Tengan.
ISBN: 978-85-244-0312-5, Projeto Euclides, Impa, 2010.

The eletronic version is not available yet. The book can be bought from IMPA.

Olimpíadas Brasileiras de Matemática, 9a a 16a, Problemas e resoluções

In portuguese. With Carlos G. Moreira, Edmilson Motta, Eduardo Tengan, Luiz Amâncio and Paulo Rodrigues.
ISBN 85-85818-19-0, Sociedade Brasileira de Matemática, Rio de Janeiro, 2003.

The eletronic version is not available yet. The book can be bought from SBM.

Tópicos em Matemática Quântica

In portuguese. With Derek Hacon, George Svetlichny, Carlos Tomei and Paulo Viana. Course text for the 22th Colóquio Brasileiro de Matemática, IMPA, 1999.

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Primos de Mersenne (e outros primos muito grandes)

In portuguese. With Carlos Gustavo T. de A. Moreira. Course text for the 22th Colóquio Brasileiro de Matemática, IMPA, 1999.

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Funções do plano no plano

In portuguese. With Iaci Malta and Carlos Tomei. Course text for the 19th Colóquio Brasileiro de Matemática, IMPA, 1993.

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Tópicos em Jogos Combinatórios

In portuguese. Course text for the 18th Colóquio Brasileiro de Matemática, IMPA, 1991.

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