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SUMMARY:Masaki Taniguchi (iTHEMS/RIKEN\, Japan)
DTSTART:20201127T120000Z
DTEND:20201127T124000Z
DTSTAMP:20260422T225923Z
UID:GTWorkshopTurkey/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GTWorkshopTu
 rkey/1/">Local equivalence in instanton Floer theory</a>\nby Masaki Tanigu
 chi (iTHEMS/RIKEN\, Japan) as part of Geometry & Topology Workshop Turkey\
 n\n\nAbstract\nRecently\, two kinds of real-valued homology cobordism inva
 riants of oriented homology 3-spheres were introduced by Daemi and Nozaki-
 Sato-Taniguchi. Their methods are based on quantitative constructions of i
 nstanton Floer homology. We develop local equivalence theory in the settin
 g of “quantitative instanton Floer theory”. From this viewpoint\, we g
 ive several new real-valued homology cobordism invariants and prove a conn
 ected sum formula for Daemi’s invariants. As applications\, we give seve
 ral new facts on the homology cobordism group. This is joint work with Ali
 akbar Daemi and Kouki Sato.\n
LOCATION:https://researchseminars.org/talk/GTWorkshopTurkey/1/
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SUMMARY:Marco Golla (CNRS\, University of Nantes\, France)
DTSTART:20201127T130500Z
DTEND:20201127T134500Z
DTSTAMP:20260422T225923Z
UID:GTWorkshopTurkey/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GTWorkshopTu
 rkey/2/">Surgeries along torus knots bounding rational balls</a>\nby Marco
  Golla (CNRS\, University of Nantes\, France) as part of Geometry & Topolo
 gy Workshop Turkey\n\n\nAbstract\nA classical question of Casson asks whic
 h 3-manifolds bound 4-manifolds with the rational homology of a ball (also
  known as "rational balls"). Motivated by results on singular curves in th
 e complex projective plane\, we study Casson's question for 3-manifolds ob
 tained as positive\, integral surgeries along positive torus knots and the
 ir cables. For torus knot we obtain a complete answer\, using a combinatio
 n of Donaldson's theorem and Heegaard Floer homology. This is joint work w
 ith Paolo Aceto\, Kyle Larson\, and Ana G. Lecuona (arXiv:2008.06760).\n
LOCATION:https://researchseminars.org/talk/GTWorkshopTurkey/2/
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SUMMARY:Irving Dai (MIT\, United States)
DTSTART:20201127T141000Z
DTEND:20201127T145000Z
DTSTAMP:20260422T225923Z
UID:GTWorkshopTurkey/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GTWorkshopTu
 rkey/3/">Corks\, involutions\, and Heegaard Floer homology</a>\nby Irving 
 Dai (MIT\, United States) as part of Geometry & Topology Workshop Turkey\n
 \n\nAbstract\nWe introduce and study a set of Floer-theoretic invariants a
 imed at detecting corks. Our invariants obstruct the extension of a given 
 involution over any homology ball\, rather than a particular contractible 
 manifold. As an application\, we define a modification of the homology cob
 ordism group which takes into account an involution on each homology spher
 e\, and prove that this admits an infinite-rank subgroup of strongly non-e
 xtendable corks. Using our invariants\, we establish several new families 
 of corks and prove that various known examples are strongly non-extendable
 . This is joint work with Matt Hedden and Abhishek Mallick.\n
LOCATION:https://researchseminars.org/talk/GTWorkshopTurkey/3/
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