Geometric Topology Seminar on July 8
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Sergey Melikhov
Jul 4, 2025, 3:56:47 PMJul 4
to Geometric Topology Seminar Mailing List, benjami...@univ-amu.fr
Geometric Topology Seminar
Tuesday (!!!), July 8, 15:30 (!!!) Moscow time
Link for connecting to the seminar: https://mian.ktalk.ru/j1xwg956wc7a
"PIN code": The number of homotopy classes of maps from the Russian
word ПЁС to the Russian word ЁЖ (where a word is understood as the
subset of the plane formed by its letters)
Benjamin Audoux (Aix-Marseille University)
Cut-diagrams and applications to knotted surfaces and link-maps II
Abstract: In this second talk, I will resume the presentation of
cut-diagrams. I will more precisely focus on the (self-)singular case
and its application to some higher order generalizations of Kirk
invariant for link-maps.
Video of the first part of the talk: https://www.mathnet.ru/eng/present46607
-------------------------------------
Seminar webpage: https://www.mathnet.ru/eng/conf192
Tuesday (!!!), July 8, 15:30 (!!!) Moscow time
Link for connecting to the seminar: https://mian.ktalk.ru/j1xwg956wc7a
"PIN code": The number of homotopy classes of maps from the Russian
word ПЁС to the Russian word ЁЖ (where a word is understood as the
subset of the plane formed by its letters)
Benjamin Audoux (Aix-Marseille University)
Cut-diagrams and applications to knotted surfaces and link-maps II
Abstract: In this second talk, I will resume the presentation of
cut-diagrams. I will more precisely focus on the (self-)singular case
and its application to some higher order generalizations of Kirk
invariant for link-maps.
Video of the first part of the talk: https://www.mathnet.ru/eng/present46607
-------------------------------------
Seminar webpage: https://www.mathnet.ru/eng/conf192
Sergey Melikhov
Jul 9, 2025, 8:44:55 PMJul 9
to Geometric Topology Seminar Mailing List
Friday, July 11, 19:00 (!!!) Moscow time
Link for connecting to the seminar: https://mian.ktalk.ru/j1xwg956wc7a
"PIN code": The number of homotopy classes of maps from the Russian
word ПЁС to the Russian word ЁЖ (where a word is understood as the
subset of the plane formed by its letters)
Fredric Ancel (University of Wisconsin at Milwaukee)
Rolfsen’s Conjecture and wild knots that pierce wild disks
(joint work with S. Melikhov)
Abstract: Rolfsen’s Conjecture (1974): Every knot (tamely or wildly
embedded S^1) in S^3 is non-ambiently isotopic to an unknot. Field
medalist Mike Freedman has singled out this striking unresolved
conjecture about manifolds as the one with the simplest statement. We
will discuss the status of this conjecture including the following
results. In 1976, Charles Giffen achieved a partial resolution of
Rolfsen’s Conjecture which has been updated and extended by S.
Melikhov and myself. Also, Melikhov has recently found remarkable
examples showing that analogue of Rolfsen’s Conjecture for 2-component
links is false. An easily proved folk theorem asserts that every knot
in S^3 that pierces a tame disk is non-ambiently isotopic to an
unknot. We will show that the same conclusion holds for knots in S^3
that pierce wild disks. Also, we will exhibit a wild knot in S^3 that
pierces a wild disk but pierces no tame disks, thereby showing that
the
previously stated result has non-trivial applications.
Link for connecting to the seminar: https://mian.ktalk.ru/j1xwg956wc7a
"PIN code": The number of homotopy classes of maps from the Russian
word ПЁС to the Russian word ЁЖ (where a word is understood as the
subset of the plane formed by its letters)
Rolfsen’s Conjecture and wild knots that pierce wild disks
(joint work with S. Melikhov)
Abstract: Rolfsen’s Conjecture (1974): Every knot (tamely or wildly
embedded S^1) in S^3 is non-ambiently isotopic to an unknot. Field
medalist Mike Freedman has singled out this striking unresolved
conjecture about manifolds as the one with the simplest statement. We
will discuss the status of this conjecture including the following
results. In 1976, Charles Giffen achieved a partial resolution of
Rolfsen’s Conjecture which has been updated and extended by S.
Melikhov and myself. Also, Melikhov has recently found remarkable
examples showing that analogue of Rolfsen’s Conjecture for 2-component
links is false. An easily proved folk theorem asserts that every knot
in S^3 that pierces a tame disk is non-ambiently isotopic to an
unknot. We will show that the same conclusion holds for knots in S^3
that pierce wild disks. Also, we will exhibit a wild knot in S^3 that
pierces a wild disk but pierces no tame disks, thereby showing that
the
previously stated result has non-trivial applications.
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