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UID:6964@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20190930T140000
DTEND;TZID=Europe/Paris:20190930T150000
DTSTAMP:20241120T202637Z
URL:https://www.i2m.univ-amu.fr/evenements/definable-homology-protorus-rig
 idity-and-cohomological-classification/
SUMMARY:Jeffrey Bergfalk (UNAM\, Mexico): Definable homology\, protorus rig
 idity\, and cohomological classification
DESCRIPTION:Jeffrey Bergfalk: The history of algebraic topology might be ro
 ughly summarized as the development of finer and finer invariants for dist
 inguishing between topological spaces. It is all the more striking\, then\
 , that two of the most canonical such invariants — the homology and coho
 mology groups of a space — are so typically approached as discrete objec
 ts\, i.e.\, as groups bearing only a trivial or essentially irrelevant top
 ology. This is surprising because the topology of a space often naturally 
 induces a topology on each of the chain and cochain groups from which the 
 homology and cohomology groups of that space\, respectively\, are computed
 . By neglecting the extra information about spaces that these topologies r
 epresent\, algebraic topologists forego a conspicuous opportunity to refin
 e two of their most prominent classes of invariants\, and this forebearanc
 e is in utter contrast with the larger impulse of their field.\n\nOf cours
 e\, there are mathematical and historical reasons for this neglect\, and o
 urs is a talk essentially about them. In other words\, we will discuss the
  challenges to making good use of the above-mentioned group topologies —
  but we will also discuss ways of overcoming these challenges\, and some o
 f the rewards to be reaped when one does. Our tools for doing so are drawn
  from descriptive set theory\, but we will presume of our audience no part
 icular knowledge of this field or of algebraic topology\; in short\, the s
 peaker intends a general mathematical audience talk on his recent joint wo
 rk with Martino Lupini and Aristotelis Panagiotopoulos on all of these top
 ics.\n\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Jeff_Bergfalk.jpg
CATEGORIES:Séminaire,Dynamique et Topologie
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DTSTART:20190331T030000
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