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Published Books

• J. Cuntz, G. Cortiñas, M. Karoubi, R. Nest. K-Theory and Noncommutative Geometry: Connections and Applications to Other Areas of Mathematics. European Mathematical Society Publishing House, 2008. Publisher's website
• P. F. Baum, G. Cortiñas, R. Meyer, R. Sánchez-García, M. Schlichting, B. Toën. Topics in algebraic and topological K-theory. Springer Lecture Notes in Mathematics 2008. Publisher's website  pdf
  

Published Papers (since 2003)

2012

• I. Heckenberger, A. Lochmann, L. Vendramin, Braided racks, Hurwitz  orbits and Nichols algebras with many cubic relations. Transform. Groups 17 (2012), no. 1, 157-194. arXiv

2011

• G. Cortiñas, C. Haesemeyer, M. E. Walker, C. Weibel.  A negative answer to a question of Bass.  Proc. Amer. Math. Soc., 139(4):1187-1200, (2011). arXiv
• M. Graña, I. Heckenberger, L. Vendramin. Nichols algebras with many quadratic relations. Adv. Math. 227 (2011), no. 5, 1956-1989. arXiv
• N. Andruskiewitsch, F. Fantino, M. Graña, L. Vendramin. Pointed Hopf algebras over the sporadic simple groups, Journal of Algebra 325 (2011) pp. 305-320. arXiv.
  

• N. Andruskiewitsch, F. Fantino, M. Graña, L. Vendramin. The logbook of Pointed Hopf algebras over the sporadic simple groups, Journal of Algebra 325 (2011) pp. 282-304. arXiv.
  
• N. Andruskiewitsch, F. Fantino, G. García, L. Vendramin, On Nichols algebras associated to simple racks. Contemp. Math. 537 (2011) 31-56. arXiv
• N. Andruskiewitsch, F. Fantino, M. Graña, L. Vendramin. Finite-dimensional pointed Hopf algebras with alternating groups are trivial. Ann. Mat. Pura Appl. (4) 190 (2011), no. 2, 225-245. arXiv
• G. Carboni, J. A. Guccione, J. J. Guccione. Cohomology ring of differential operator rings. J. Algebra 339 (2011), 55--79. arXiv.
• J. A. Guccione, J. J. Guccione, C. Valqui. Twisted planes. Communications in Algebra 38(5) (2010) 1930-1956. arXiv
• J. A. Guccione, J. J. Guccione, C. Valqui, Universal deformation formulas and braided module algebras, Journal of Algebra 330 (2011) 263–297. arXiv

2010

• N. Andruskiewitsch, F. Fantino, M. Graña, L. Vendramin. Pointed Hopf algebras over some sporadic simple groups.  C. R. Math. Acad. Sci. Paris 348 (2010) pp. 605-608. arXiv.

• G.  Cortiñas. Algebraic v. topological K-theory: a friendly match. In Topics in algebraic and topological K-theory. Springer Lecture Notes in Mathematics 2008.  arXiv
• G. Cortiñas, C. Haesemeyer, M.E. Walker, C. Weibel. Bass' NK groups and cdh-fibrant Hochschild homology. Inventiones Mathematicae 181 (2), pp. 421-448. arXiv
• S. Freyre, M. Graña, L. Vendramin. On Nichols algebras over PGL(2,q) and PSL(2,q). J. Algebra Appl., Vol. 9, No. 2 (2010) 195–208. arXiv

• G. Carboni, J. A. Guccione, J. J. Guccione. Cyclic homology of Hopf crossed products. Advances in Mathematics, 223 (2010), 840--872.
  
• N. Andruskiewitsch, F. Fantino, G. García, L. Vendramin, On twisted homogeneous racks of type D. Rev. Unión Mat. Argent. 51 2(2010) 1-16. arXiv
  

2009

• P. Ara, M. Brustenga, G. Cortiñas. K-theory of Leavitt path algebras.  Münster Journal of Mathematics, 2 (2009), 5--34. arXiv

• G. Carboni, J. A. Guccione, J. J. Guccione. The cyclic homology of monogenic extensions in the noncommutative setting. Journal of Algebra 321 (2009), 404-428. arXiv.
• G. Cortiñas, C. Haesemeyer, M. E. Walker, C. Weibel. The K-theory of toric varieties. Trans. Amer. Math. Soc. 361 (2009), 3325-3341. arXiv
  
• G. Cortiñas, C. Haesemeyer, C. Weibel. Infinitesimal cohomology and the Chern character to negative cyclic homology. Math Annalen 344 (2009) 891-922. arXiv
• G. Cortiñas, C. Weibel. Relative Chern characters for nilpotent ideals.  Algebraic Topology. The Abel Symposium 2007. Baas, N.; Friedlander, E.M.; Jahren, B.; Østvær, P.A. (Eds.). Springer, 2009; pp 61-82.

2008

• G. Cortiñas, C. Haesemeyer, M. Schlichting, C. Weibel. Cyclic homology, cdh-cohomology and negative K-theory. Annals of Math. 167 (2008) 549-573. arXiv

• G. Cortiñas, C. Haesemeyer, C. Weibel. K-regularity, cdh-fibrant Hochschild homology, and a conjecture of Vorst. Journal of the Amer. Math. Soc. 21 (2008), 547--561. arXiv
  
• G. Cortiñas, A. Thom. Comparison between algebraic and topological K-theory of locally convex algebras. Advances in Mathematics, 218 (2008), 266-307. arXiv
• M. Farinati, J.A. Guccione, J.J. Guccione. The cohomology of monogenic extensions in the noncommutative setting.  Journal of Algebra 319 (2008), 5101-5124. arXiv

2007

• G. Cortiñas, A. Thom. Bivariant algebraic K-theory. J. reine angew. Math. 510 (2007) 71-124. arXiv

• M. Da Rocha, J. A. Guccione, J. J. Guccione. Braided module and comodule algebras, Galois extensions and elements of trace 1. Journal of Algebra 307 (2), (2007) 727-768 .
• S. Freyre, M. Graña, L. Vendramin. On Nichols algebras over SL(2,q) and GL(2,q). J. Math. Phys. 48, 123513 (2007). arXiv.
  
• M. Graña, I. Heckenberger. On a factorization of graded Hopf algebras using Lyndon words J. Algebra 2007 314 324-343 pdf dvi
• M. Graña, J. J. Guccione, J. A. Guccione. Decomposition of some pointed Hopf algebras given by the canonical Nakayama automorphism J. Pure Appl. Algebra 2007 210 493-500 pdf dvi
• M. Graña, J. P. Pinasco. Discrete Scale Invariance in Scale Free Graphs Physica A 2007 380 601-610 pdf

2006

• G. Acosta, M. Graña, J. P. Pinasco. Condition numbers and scale free graphs The European Physical Journal B 2006 53 381-385 e-version pdf
• G. Cortiñas. The obstruction to excision in K-theory and in cyclic homology. Invent. Math. 454 (2006) 143-173. arXiv
• J. A. Guccione y J. J. Guccione. Relative cyclic homology of square zero extensions. Journal fur die reine und angewandte Mathematik 600, 51-80 (2006).

2005

• J.S. Carter, M. Elhamdadi, M. Graña, M. Saito Cocycle Knot Invariants from Quandle Modules and Generalized Quandle Cohomology Osaka J. Math. 42 499-541 2005 ps.gz
• C. Di Luigi, J. A. Guccione, J. J. Guccione. Brzezinski's crossed products and braided Hopf crossed products. Communications in Algebra 32, 3563-3580 (2004)
• P. Etingof, M. Graña. Quantization of non-unitary geometric classical r-matrices Math. Res. Letters 12 2,3 141-153 2005 dvi ps.gz
• M. Farinati. Hochschild duality, localization and smash products. Journal of Algebra. Volume 284, Issue 1, 1 (2005), 415-434. arXiv
• M. Graña, V. Turaev. Knot theory for self-indexed graphs Trans. Amer. Math. Soc. 357 535-553 2005 dvi ps.gz djvu

2004

• J.L. Castiglioni, G. Cortiñas. Cosimplicial versus DG-rings: a version of the Dold-Kan correspondence. J. Pure Appl. Algebra.191 (2004) 119-142. arXiv
• G. Cortiñas. The structure of smooth algebras in Kapranov's framework for noncommutative geometry. J. of Algebra 281 (2004) 679-694. arXiv
• G. Cortiñas, M. de León. Cálculos efectivos de la homología cíclica negativa de hipersuperficies con singularidades aisladas. EACA 2004: Actas de los Encuentros de Algebra Computacional y Aplicaciones, 2004. L. González Vega, T. Recio (Eds.) Universidad de Cantabria. Santander, 2004.ISBN 84-688-6988-04
• M. Farinati,  A. Solotar. G-Structure on the cohomology of Hopf algebras. Proc. Amer. Math. Soc. 132 (2004), 2859-2865. arXiv
• M. Graña. Indecomposable racks of order p2 Beiträge Algebra Geom. 45 2 665-676 2004 dvi ps.gz

2003

• N. Andruskiewitsch, M. Graña. Examples of liftings of Nichols algebras over racks Téories d'homologie, repésentations et algèbres de Hopf AMA Algebra Montp. Announc. Paper 1, 6 pp. (electronic) 2003 dvi ps.gz
• N. Andruskiewitsch, M. Graña. From racks to pointed Hopf algebras Adv. Math. 178 2 177-243 2003 ps.gz
• G. Cortiñas, C. Valqui. Excision in bivariant periodic cyclic homology: a categorical approach. 30 (2003) 167-201. arXiv
• G. Cortiñas. De Rham and infinitesimal cohomology in Kapranov's model for noncommutative algebraic geometry. Compositio Mathematica 136 (2003) 171-203 arXiv
• P. Etingof, M. Graña. On rack cohomology J. Pure Appl. Algebra 177 1 49-59 2003 dvi ps.gz
• M. Farinati. On the derived invariance of cohomology theories for coalgebras. Algebras and Representation Theory 6(3) pp. 303-331 (2003). arXiv
• J. A. Guccione, J. J. Guccione. Hochschild cohomology of Frobenius algebras. Proceedings of the American Mathematical Society 132 (5), 1241-1250 (2003).
• J. A. Guccione, J. J. Guccione. Theory of braided Hopf crossed products. Journal of Algebra 261 (1), 54-101 (2003)

Articles accepted for publication

• P. Ara, G. Cortiñas. Tensor products of Leavitt path algebras.   Proc. Amer. Math. Soc., to appear.  arXiv
• G. Cortiñas, C. Haesemeyer, M. E. Walker, C. Weibel. K-theory of cones of smooth varieties.  Journal of Algebraic Geometry, to appear. arXiv
• G. Cortiñas, G. Tartaglia. Operator ideals and assembly maps in K-theory.  Proc. Amer. Math. Soc., to appear. arXiv
• G. Cortiñas, A. Thom. Algebraic geometry of topological spaces I. To appear in Acta Mathematica. arXiv
• J. A. Guccione, J. J. Guccione, C. Valqui, On the centralizers in the Weyl algebra, To appear in Proceedings of the American Mathematical Society. arXiv
• L. Vendramin, Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent. To appear in Proceedings of the American Mathematical Society. arXiv
• L. Vendramin, On the classification of quandles of low order. To appear in J. Knot Theory Ramifications. arXiv

Preprints

• G. Carboni, J. A. Guccione, J. J. Guccione, C. Valqui. Cyclic homology of braided Hopf crossed products. arXiv
  
• S. D. Corti, J. A. Guccione, J. J. Guccione. Braided Sweedler cohomology. arXiv.
• G. Cortiñas, E. Ellis. Isomorphism conjectures with proper coefficients. arXiv
• G. Cortiñas, C. Haesemeyer, M.E. Walker, C. Weibel. Toric varieties, monoid schemes and $cdh$ descent. arXiv

• M. Farinati, P. Jancsa. Trivial Central Extensions of Lie Bialgebras. arXiv
  
• M. Farinati, P. Jancsa. Three dimensional real Lie bialgebras. arXiv

• M. Graña, J.A. Guccione, J.J. Guccione. How to disentangle two braided Hopf algebras. arXiv
• J. A. Guccione, J. J. Guccione. A characterization of quiver algebras based on double derivations. arXiv
• J. A. Guccione, J. J. Guccione, C. Valqui. Non commutative truncated polynomial extensions. arXiv
• J. A. Guccione, J. J. Guccione, C. Valqui. The Dixmier conjecture and the shape of possible counterexamples. arXiv
  
• P.M. Hajac, A. Kaygun, C. Pagani, B. Zielinski. Finite closed coverings of compact quantum spaces. arXiv
• F. Fantino, L. Vendramin, On twisted conjugacy classes of type D in sporadic simple groups, arXiv