Dr. Antonio Viruel
D. Álgebra, Geometría y Topología
Campus de Teatinos, Universidad de Málaga
29071 Málaga

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E-mail: viruel	@agt.cie.uma.es
E-mail: viruel	@uma.es

Phone: (+34) 952 13 20 09

Research

Here you have the page dedicated to my mathematical research. It is divided in four sections: Research Interest, Publications, Theses, Preprints and Work in Progress. You may find interesting to take a look to my author profile at these sites:

Research Interest:

I am what people call an algebraic topologist. My research is focus on the interactions between Group Theory and Homotopy Theory, and it follows different lines:

Homotopy theory of loop spaces: By homotopy theory of loop spaces I mean "homotopy group theory", "p-compact groups", or "p-local finite groups", and related stuff as cohomology of groups. This implies that sometimes I have to work with honest groups. I develop this research as part of the Barcelona Algebraic Topology Group.

Homotopy invariants and self homotopy equivalences: This is a more classical branch of Algebraic Topology in which I am also interested. My research is nowadays mainly focus in understanding the group of self homotopy equivalences of a space. This research is developed jointly with Cristina Costoya as part of the Xunta de Galicia research project "Representación Homotópica de Grupos" (EM2013/016).

All these approaches to Homotopy Theory are included in:

The Research Training Network Modern Homotopy Theory supported by the European Commission (EEC HPRN-CT-1999-00119).
Groupement de Recherche Européen Topologie algébrique supported by the Centre National de la Reserche Scientifique (G.D.R.E. C.N.R.S. N° 1110).
The Junta de Andalucía research group "Geometría y Topología Universidad de Málaga" (FQM-213).
The research FEDER-MCI grant MTM2013-41768-P.
The European Science Foundation Research Networking Program Applied and Computational Algebraic Topology (09-RNP-064 ACAT).
The Junta de Andalucía research grant "Geometrical and topological methods in Economy, Robotics and Theoretical Physics" (P07-FQM-2863)

I am a proud member of the following mathematical research networks:

RET: Red Española de Topología (Spanish Topology Network). It has a facebook page!
IBG: Red Ibérica de Teoría de Grupos (Iberian Network of Group Theory).
NcAlg: Red Temática de Álgebra no Conmutativa (Noncommutative Algebra Thematic Network).

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Publications:

These are my publications by inverse chronological order. For each publication, the following links may be available:

[MathSciNet MR]: Link to the AMS Math Review of the paper. You may need a subscription to access to the actual review.
[ZMath]: Link to the Zentralblatt Math Review of the paper. You may need a subscription to access to the actual review.
[Article]: Link to the article in the journal web page. You may need a subscription to access to the actual article.
[Preprint-XX]: Link to the preprint version of the paper at the archive XX. Notice that there could be big differences between this version and the final version of the article.
[Cited by]: Link to a list of papers that quoted the paper (it should open in a different window). Please, let me know if you ever referred to any of my works.
[DJVU]: Link to a scan of the article, in DjVu format. You may need a pluging or viewer to read these files. You can learn about the DjVu format from Wikipedia.

[33]	*"Smooth torus actions are described by a single vector field"*, to appear in Rev. Mat. Iberoam. F.J. Tiruel, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[32]	*"Fine gradings on e₆"*, Publicacions Matemàtiques 60 (2016), 113-170. C. Draper, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[31]	*"On Thompson's p-complement theorems for saturated fusion systems"*, Kyoto Journal of Mathematics 55 (2015), 617-626. J. González-Sánchez, A. Ruiz, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[30]	*"Rational homotopy theory for computing colorability of simplicial complexes"*, Applicable Algebra in Engineering, Communication and Computing 26 (2015), 207-212. C. Costoya, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[29]	*"Faithful actions on Commutative Differential Graded Algebras and the Group Isomorphism Problem"*, The Quarterly Journal of Mathematics 65 (2014), 857-867 C. Costoya, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[28]	*"Every finite group is the group of self homotopy equivalences of an elliptic space", Acta Mathematica 213* (2014), 49-62. C. Costoya, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[27]	*"Nilpotent p-local finite groups"*, Arkiv för Matematik 52 (2014), 203-225. J. Cantarero, J. Scherer, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[26]	*"Finite C^∞-actions are described by a single vector field"*, Rev. Mat. Iberoam. 30 (2014), 317-330. F.J. Turiel, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[25]	*"Cohomological uniqueness of some p-groups"*, Proc. of the Edinburgh Math. Soc. 56 (2013), 449-468. A. Díaz, A. Ruiz, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[24]	*"Cohomological uniqueness, Massey products and the modular isomorphism problem for 2-groups of maximal nilpotency class", Transactions AMS. 365* (2013), 3729-3751. A. Ruiz, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Preprint-UAB] [Cited by] [DJVU]
[23]	*"Inductive LS cocategory and localisation", Manuscripta Mathematica 140* (2013), 295-302. C. Costoya, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[22]	*"Nilpotency of self homotopy equivalences with coefficients"*, Annales de l'Institut Fourier 61 (2011), 351-364. M. Cuvillez, A. Murillo, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[21]	*"Fine Gradings on the Lie algebra d₄"*, Forum Mathematicum 22 (2010), 863-877. C. Draper, C. Martín, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[20]	*"On the homotopy type of the non-completed classifying space of a p-local finite group"*, Forum Mathematicum 21 (2009), 723-757. A. Libman, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Benson] [Cited by] [DJVU]
[19]	*"Group gradings on o(8,C)"*, Reports on Mathematical Physics 61 (2008), 263-278. C. Draper, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[18]	*"The classification of p-compact groups for p odd", Annals of Math. 167* (2008), 95-210. K. Andersen, J. Grodal, J.M. Møller, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[17]	*"The group of self homotopy equivalences of some localized aspherical complexes", Math. Nach. 281* (2008), 214-218. A. Garvín, A. Murillo, J. Remedios, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[16]	*"All p-local finite groups of rank 2, p odd", Transactions AMS 359* (2007), 1725-1764. A. Díaz, A. Ruiz, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[15]	*"Simplectic groups are N-determined 2-compact groups", Fundamenta Math. 192* (2006) , 121-139. A. Vavpetic, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[14]	*"Non simple localization of finite simple groups", J. of Algebra 305* (2006), 765-774. J.L. Rodríguez, J. Scherer, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[13]	*"On the mod p cohomology of BPU(p)", Transactions AMS 357* (2005), 4517-4532. A. Vavpetic, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Hopf] [Cited by] [DJVU]
[12]	*"Preservation of perfectness and acyclicity: Berrick's and Casacuberta's universal acyclic space localized at a set of primes"*, Forum Mathematicum 17 (2005), 67-75. J.L. Rodríguez, J. Scherer, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Arxiv] [Cited by] [DJVU]
[11]	*"The classification of p-local finite groups over the extraspecial group of order p³ and exponent p", Math. Z. 248* (2004), 45-65. A. Ruiz, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Hopf] [Cited by] [DJVU]
[10]	*"Projective unitary groups are totally N-determined p-compact groups", Math. Proceedings of Cambridge Philos. Society 136* (2004), 75-88. C. Broto, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Cited by] [DJVU]
[9]	*"On the Homotopy type of the Classifying Space of the Exceptional Lie Group F₄", Manuscripta Math. 107* (2002), 521-540. A. Vavpetic, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Hopf] [Cited by] [DJVU]
[8]	*"Mod 3 homotopy uniqueness of BF₄"*, J. Math. Kyoto University 41 (2001), 769-793. A. Viruel. [MathSciNet MR] [ZMath] [Article] [Cited by] [DJVU]
[7]	*"Lusternik-Schnirelmann cocategory: A Whitehead dual approach", Cohomological Methods in Homotopy Theory, Progress in Math. 196*, Birkhäuser Verlag (2001), 323-347. A. Murillo, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Cited by] [DJVU]
[6]	*"Nilpotency and localization of groups of fibre homotopy equivalences", Contemp. Math. 274* (2001), 145-157. A. Garvín, A. Murillo, P. Pavešic, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Cited by] [DJVU]
[5]	*"E₈ is a totally N-determined 5-compact group", Contemp. Math. 265* (2000), 223-231. A. Viruel. [MathSciNet MR] [ZMath] [Article] [Cited by] [DJVU]
[4]	*"On the mod 3 homotopy type of the classifying space of a central product of SU(3)'s"*, J. Math. Kyoto University 39 (1999), 249-275. A. Viruel. [MathSciNet MR] [ZMath] [Article] [Cited by] [DJVU]
[3]	*"An extension of Miller's version of the De Rham theorem with any coefficients"*, Homotopy and Geometry, Banach Center Pub. 45 (1998), 169-176. A. Garvín, L. Lechuga, A. Murillo, V. Muñoz, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Cited by] [DJVU]
[2]	*"Homotopy Uniqueness of BG₂"*, Manuscripta Math. 95 (1998), 471-497. A. Viruel. [MathSciNet MR] [ZMath] [Article] [Preprint-Benson] [Cited by] [DJVU]
[1]	*"Homotopy Uniqueness of BPU(3)"*, Proc. of Symposia in Pure Maths. 63 (1998), 85-93. C. Broto, and A. Viruel. [MathSciNet MR] [ZMath] [Article] [Cited by] [DJVU]

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Theses:

These are the two (Master and PhD) theses I have written in chronological order. Someone may find something useful in them:

[1]	*"La categoría de Lusternik-Schnirelmann"* (under the supervision of A. Murillo), Master Thesis 1992. [DJVU-No OCR]
[2]	*"Homotopy uniqueness of classifying spaces of compact Lie groups"* (under the supervision of C. Broto), PhD. Thesis 1996. [DJVU]

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Preprints:

By chronogical order of preparation:

"A Torus Theorem for homotopy nilpotent groups"
C. Costoya, J. Scherer, and A. Viruel
[Preprint-Arxiv]
"On the realizability of group actions"
C. Costoya, and A. Viruel
[Preprint-Arxiv]
"Homotopically rigid Sullivan algebras and its applications"
C. Costoya, D. Méndez and A. Viruel
[Preprint-Arxiv]
"A cohomological characterization of nilpotent fusion systems"
A. Díaz Ramps, A. Espinosa Baro and A. Viruel
[Preprint-Arxiv]

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Work in Progress:

Some stuff that should be finished soon (or not):

"On a Borel-Serre's theorem for mod p representation" joint with K. Andersen.
"A topological approach to the modular isomorphism problem" joint with A. Ruiz.
"On the index for fixed point free G-spaces" joint with F. Gómez.
"How many laws has to impose a dictator?" joint with J.A. Crespo.
"Is it really hard the job of a dictator?" joint with J.A. Crespo and J. Scherer.
"Rigid full inclusions of digraphs and geometrical applications" joint with C. Costoya and R. Fernández.

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