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CATEGORIES:Conferences/Seminars/Lectures
DESCRIPTION:Featured Speaker: Piotr Suwara (MIT)\n\nTitle: Constructing Flo
er homologies: Morse theory vs. infinite-dimensional cycles\n\nAbstract: Fl
oer's idea of obtaining homological invariants in symplectic and low-dimens
ional topology via a construction of a Morse-Smale-Witten chain complex\, c
omputing the "middle-dimensional homology" of some specific infinite-dimens
ional spaces\, led to the construction of groundbreaking invariants known c
ollectively under the name of "Floer homology". Soon after the emergence of
these ideas Atiyah suggested thinking about Floer theories as describing t
he homology of "semi-infinite dimensional cycles". Following the (unpublish
ed) work of Mrowka and Ozsváth\, Lipyanskiy defined Floer homology and Floe
r bordism groups using semi-infinite dimensional cycles for a class of so-c
alled Floer spaces. The construction is appealing since it does not require
considering the compactification of moduli spaces of trajectories\, which
is a subtle analytical procedure\, or perturbing the Floer functional\, whi
ch is usually a serious obstacle for defining equivariant Floer homologies.
I will describe the construction of this semi-infinite Floer homology and
argue why it recovers the tilde flavor (i.e. the non-equivariant version) o
f Monopole Homology (assuming no reducible solutions).
DTEND:20200309T200000Z
DTSTAMP:20241115T032851Z
DTSTART:20200309T190000Z
GEO:42.358262;-71.090045
LOCATION:Building 2\, 2-449
SEQUENCE:0
SUMMARY:Geometry and Topology Seminar
UID:tag:localist.com\,2008:EventInstance_32875162830605
URL:https://calendar.mit.edu/event/geometry_and_topology_seminar_5382
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