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SUMMARY:Maria Pe Pereira (Universidad Complutense de Madrid)
DTSTART:20210504T140000Z
DTEND:20210504T150000Z
DTSTAMP:20260423T021347Z
UID:ZAG/117
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ZAG/117/">Mo
 derately Discontinuous Algebraic Topology</a>\nby Maria Pe Pereira (Univer
 sidad Complutense de Madrid) as part of ZAG (Zoom Algebraic Geometry) semi
 nar\n\n\nAbstract\nAn algebraic or complex analytic subset in C^n has 2 na
 tural metrics: the outer metric (restriction of the euclidean metric) and 
 the inner metric (natural extension of the riemannian metric on the smooth
  part). These metrics considered up to bilipschitz mappings are analytic i
 nvariants\, that is\, they do not depend on the complex analytic embedding
 .\nRecently there is an intense activity in bilipschitz geometry of germs 
 and degenerations\, enriching and providing finer information on\nproblems
  that were studied previously from the topological viewpoint (for multipli
 city invariance of the germ or certain equisingularity notions).\nIn the w
 orks [1] and [2] we develop a new metric algebraic topology\, called the M
 oderately Discontinuous Homology and Homotopy\, in the context of subanaly
 tic germs in R^n (with a supplementary metric structure) and more generall
 y of (degenerating) subanalytic families. This theory captures bilipschitz
  information\, or in other words\, quasi isometric invariants\, and aims t
 o codify\, in an algebraic way\, part of the bilipschitz geometry.\nA suba
 nalytic germ is topologically a cone over its link and the moderately disc
 ontinuous theory captures the different speeds\, with respect to the dista
 nce to the origin\, in which the topology of the link collapses towards th
 e origin. Similarly\, in a degenerating subanalytic family\, it captures t
 he different speeds of collapsing with respect to the family parameter.\nT
 he MD algebraic topology satisfies all the analogues of the usual theorems
  in Algebraic Topology: long exact sequences for the relative case\, Mayer
  Vietoris and  Seifert van Kampen for special coverings...\nIn this talk\,
  I will present the most important concepts in the theory and some results
  or applications that we got until the present.\n[1] (with J. Fernandez de
  Bobadilla\, S. Heinze\, E. Sampaio) Moderately discontinuous homology. To
  appear in  Comm. Pure App. Math.. Available in  arXiv: 1910.12552\n[2]   
 (with J. Fernández de Bobadilla\, S. Heinze) Moderately discontinuous hom
 otopy. Submitted. Available in ArXiv:2007.01538\n
LOCATION:https://researchseminars.org/talk/ZAG/117/
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