Martintxo Saralegi-Aranguren

Most significant publications

Abstracts

Perverse homotopy

·       Perverse homotopy groups
(With D. Chataur and D. Tanré). Arxiv

·       Homotopy truncations of homotopically stratified spaces
Proceedings of the A.M.S. 152 (2024), 1319-1332.
(With D. Chataur and D. Tanré). Arxiv

Intersection (co)homology

·       Simplicial intersection homology revisited
(With D. Chataur and D. Tanré). Arxiv

·       A reasonable notion of dimension for singular intersection homology
Accepted for publication in Journal of Homotopy and Related Structures
(With D. Chataur and D. Tanré). Arxiv

·       Addendum to ”Refienment invariance of intersection (Co)homologies”
Homology, Homotopy and Applications 26(2024), 259-274.Arxiv

·       Refinement invariance of intersection (co)homologies
Homology, Homotopy and Applications 23 (2021), 311-340. Arxiv

·       Poincaré duality, cap products and Borel-Moore intersection Homology
Quarterly Journal of Mathematics 71(2020), 943-958
(With D. Tanré). Arxiv

·       Blown-up intersection cochains and Deligne's sheaves
Geometriæ Dedicata 204(2020), 315-337.
(With D. Chataur and D. Tanré). Arxiv

·       Variations on Poincaré duality for intersection homology
Enseignement Mathématique 65(2020), 117-154.
(With D. Tanré). Arxiv

·       Intersection homology. General perversities and topological invariance.
Illinois Journal of Mathematics 63(2019), 127-163.
(With D. Chataur and D. Tanré). Arxiv

·       Lefschetz duality for intersection (co)homology
Mathematische Zeitschrift 291(2019), 1-16. Arxiv

·       Poincaré duality with cap products in intersection homology
Advances in Mathematics 326(2018), 314-351.
(With D. Chataur and D. Tanré). Arxiv

·       Blown-up intersection cohomology
An alpine bouquet of algebraic topology. Contemporary Mathematics, 708(2018), 45-102.
(With D. Chataur and D. Tanré). Arxiv

·       Intersection Cohomology. Simplicial Blow-up and Rational Homotopy.
Memoirs AMS 254(2018), 1-108.
(With D. Chataur and D. Tanré). Arxiv

·       Singular decompositions of a cap-product
Proceedings of the AMS 145(2017), 3645-3656.
(With D. Chataur and D. Tanré). Arxiv

·       Steenrod squares on Intersection cohomology and a conjecture of M. Goresky and W. Pardon.
Algebraic & Geometric Topology 16(2016), 1851-1904.
(With D. Chataur and D. Tanré). Arxiv

·       De Rham intersection cohomology for general perversities.
Illinois Journal of Mathematics49(2005), 737-758.

·       Cohomologie d'intersection modérée. Un Théorè me de deRham.
Pacific Journal of Math. 169 (1995), 235-289.
(With B. Cenkl et G. Hector).

·       Homological properties of stratified spaces.
Illinois Journal of Mathematics 38(1994), 47-70.

·       Homologie d'intersection and variétés homologiques.
C.R.A.S. 314(1992), 847-851.
(With J.P. Brasselet).

·       L²-cohomologie des espaces stratifés.
Manuscripta Math. 76 (1992), 21-32. .
(With G. Hector).

·       Théorè me de de Rham pour les variétés stratifiées.
Annals of Global Anal. and Geo. 9 (1991), 211-243
(With J. P. Brasselet and G. Hector).

·       Homología de intersección: comparación para perversidades diferentes .
Actas XII Jornadas Hispano-Lusas de Matemáticas, Universidade do Minho vol. II (1987), 735-758.

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Singular riemannian foliations

 

·       Hard Lefschetz Property for S3-actions
Accepted for publication in Proceedings of the A.M.S.
(Avec J. I. Royo Prieto et R. Wolak) Arxiv

·       Hard Lefschetz Property for Isometric Flows.
Transformation Groups 29, 409–423 (2024)
(With J.I. Royo Prieto and R. Wolak). D.O.I.

·       Cohomological tautness for singular riemannian foliations
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales 143(2019), 4263-428.
(With J. I. Royo Prieto et R. Wolak). Arxiv

·       Poincaré Duality of the basic intersection cohomology of a Killing foliation.
Monatsh Math 180(2016) 145-166
(With R. Wolak). Arxiv

·       Finitness of the basic intersection cohomology of a Killing foliation.
Mathematische Zeitschrift 272 (2012), 443-457
(With R. Wolak) Arxiv

·       Cohomological tautness for Riemannian foliations.
Russ. Journal of Math. Physics 16(2009), 450-46.
(With J. I. Royo Prieto et R. Wolak). Arxiv

·       Tautness for riemannian foliations on non-compact manifolds.
Manuscripta Math. 126(2008), 177-200
(With J. I. Royo Prieto and R. Wolak). Arxiv

·       Top dimensional group of the basic intersection cohomology for singular riemannian foliations.
Bull. Polish Ac Sc. 53(2005), 429-440.
(With J. I. Royo Prieto and R. Wolak). Arxiv

·       The BIC of a singular foliation defined by an abelian group of isometries.
Ann. Polon. Math. 89 (2006), 203-246
(With R. Wolak). Arxiv

·       The BIC of a conical foliations.
Mat. Zametki 77(2005), 235--257.
Translation in Math. Notes 77(2005). 213-231
(With R. Wolak). Arxiv

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Compact Lie group actions

·       The Gysin Braid for S³-actions on manifolds
(With J.I. Royo Prieto). Arxiv

·       Smith-Gysin Sequence
Differential Geometric Structures and Applications. IWDG 2023. Springer Proceedings in Mathematics & Statistics, 440(2024), 239–248.
(With J.I. Royo Prieto and R. Wolak ). Arxiv

·       Equivariant intersection cohomology of the circle actions.
Real Academia de Ciencias Exactas, Físicas y Naturales 108(2014), 49-62.
(With J.I. Royo Prieto). Arxiv

·       The Gysin sequence for S³-actions on manifolds.
Publicationes Mathematicae Debrecen 3(2013), 275?89.
(With J.I. Royo Prieto). Arxiv

·       Intersection cohomology of circle actions.
Topology and its Applications 254(2007), 2764-2770.
(With G. Padilla). Arxiv

·       Minimal models for non-free circle actions.
Illinois Journal of Mathematics 44(2000), 784-820.
(With A. Roig).

·       Cohomologie d'intersection des actions toriques simples.
Indagationes Math. 7(1996), 389-417.

·       Gysin sequences.
Analysis and geometry in foliated manifolds
Santiago de Compostela, 1994, 207-222..

·       A Gysin sequence for semifree actions of S³.
Proceedings of the A.M.S. 118(1993), 1335-1345.

·       Intersection cohomology of S¹-actions.
(With G. Hector).
Transactions of the A.M.S. 338(1993), 263-288.

·       The Euler class for flows of isometries.
Research Notes in Math. 131(1985), 220-227.

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Others

·       Euler y un balón de fútbol.
SIGMA, Servicio Central de Publicaciones del Gobierno Vasco 36(2011), 125-135.
(With J.I. Royo Prieto).

·       A six dimensional compact symplectic solvmanifold without KŠhler structures.
Osaka J. Math. 33 (1996), 19-35.
(With M. Fern‡ndez and M. de León).

·       Cosymplectic reduction for singular momentum maps-actions.
J. Phys.A Math. Gen. 26(1993) 5032-55043.
(With M. de León).

·       Fuzzy filters.
Journal of Math. Anal. and App. 129 (1988), 560-566.
(With M. A. de Prada).

·       Una nota sobre convergencia en espacios toplógicos fuzzy.
Actas IX Jornadas Hispano-Lusas vol. II (1982), 763-766.
(With M. A. de Prada).

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Slides and Videos

·       Dos cohomologías de intersección y una conjetura de Goresky y Pardon
Seminario Topología Algebraica. Universidad Nacional Autónoma de México. México. August 2019. Slides      Video
In collaboration with D. Chataur & D. Tanré.

·       Intersection cohomologies
MPS Conference on Singularities: Geometric, Topological, and Analytic Aspects
Simons Foundation, New York (EEUU). August 2018. Slides      Video
In collaboration with D. Chataur & D. Tanré.

·       Filtered (co)-intersection Poincaré duality.
Workshop on Stratified Spaces: Perspectives from Analysis, Geometry and Topology
Fields Institute, Toronto (Canada). August 2016. Slides      Video
In collaboration with D. Chataur & D. Tanré.

·       Gysin sequence for smooth S ^3-actions
Knots, Manifolds, and Group Actions.
Slubice (Poland). Septembre, 2013. Slides
In collaboration with J.I. Royo Prieto.

·       Qu'est-ce qu'un mathématicien?
Le Tour de France des Déchiffreurs, voyage en mathématiques Video
Paroles des dechiffreurs,
interview with é. Mathéron by V. Vassallo. Video
Janvier, 2012.

The basic intersection cohomology of a singular riemannian foliation.
XVIII Encuentro de Topología
Sevilla (Spain). Octobre 2011. Slides
In collaboration with R. Wolak.

·       Sobre la Conjetura de Poincaré
Paseo en la geometría
Bilbao (Spain). April 2008. Slides

·       Minimality and singular riemannian foliations.
Primer Congreso Hispano-Francés de Matem‡áticas - Premier Congrès Franco-Espagnol de Mathématiques
Zaragoza (Spain). July 2007. Slides
In collaboration with J.I. Royo Prieto & R. Wolak.

·       The basic intersection cohomology of a singular riemannian foliation
6th Conference on Geometry and Topology
Krynica (Poland). Mai 2004. Slides
In collaboration with R. Wolak.

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Errare humanum est, perseverare diabolicum

·       Homological properties of stratified spaces.
There is an an unforgivable oblivion in the statement of Proposition 2.2.5: the perversity p must lie between the 0 perversity and the top perversity. So, one of the two main results of the paper (Theorem 4.15) also needs this hypothesis. Notice that the usual Goresky-MacPherson perversities satisfy this condition.
This error is corrected in De Rham intersection cohomology for general perversities, where tame intersection homology appears for the first time in a hidden way (see Blown-up intersection cohomology for an explict definition of this homology).

·       Blown-up intersection cohomology
There is a gap in the proof of Theorem E (b) (pag. 91): we should have proved that H(ω) is a p-allowable cochain in order to get that H(ω) is an integrating cochain of ω. But this is not true, we need another integrating cochain of ω. This is done here, where the corrections are in red..

·       Refinement invariance of intersection (co)homologies
There is an error on page 24, last formula on the 13th line from the bottom. The right writing is here, where the corrections are in red.

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