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Martintxo Saralegi-Aranguren
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Most significant publications
Abstracts
Perverse homotopy
·
Simplicial intersection homology revisited
Accepted for publication in Journal of Homotopy and
Related Structures
(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
· Perverse homotopy groups
(With D. Chataur and D. Tanré).
Arxiv
Intersection (co)homology
· Addendum to ”Refienment
invariance of intersection (Co)homologies”
Homology, Homotopy and Applications (2023) Arxiv
· A reasonable notion of dimension for singular intersection homology
(With D. Chataur and D. Tanré).
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
· Lefschetz duality 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
· 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
· The Gysin Braid for S3-actions on manifolds
(With J.I. Royo Prieto). 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 Khler
structures.
Osaka J. Math. 33 (1996), 19-35.
(With M. Fernndez 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 Matemáticas -
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.