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From Higher Invariants


Regensburg low-dimensional geometry and topology seminar

The seminar is on summer break, and will resume in November 2020.

The seminar takes place on Zoom (see information below) every Tuesday at 16:00 CET (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).

Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).

Talks in fall/winter 2020/21

Date Speaker Title Abstract
November 3 Marco Marengon (MPIM Bonn) Non-orientable knot cobordisms and torsion order in Floer homologies Given an orientable knot cobordism between classical knots K and K', Juhász, Miller, and Zemke proved an inequality involving the torsion order of the knot Floer homology of K and K' and the Euler characteristic and the number of local maxima appearing in the cobordism.

In our work, we prove analogous inequalities for unorientable knot cobordisms, using unoriented versions of instanton and knot Floer homology. Much of the subtlety in our argument lies in the fact that we need to choose more complicated decorations on the surface than the ones appearing in Juhász-Miller-Zemke's case. We also introduce unoriented versions of the band unknotting number and of the refined cobordism distance and apply our results to give bounds on these based on the torsion orders of the Floer homologies. As an application, I will exhibit a family of knots all of which bound an embedded Möbius band in B^4, but for which the unorientable refined cobordism distance from the unknot is arbitrarily large. This is joint work with Sherry Gong.

November 10 Masaki Taniguchi (Riken) Filtered instanton Floer homology and the 3-dimensional homology cobordism group We introduce a family of real-valued homology cobordism invariants r_s(Y) of oriented homology 3-spheres. The invariants r_s(Y) are based on a quantitative construction of filtered instanton Floer homology. Using our invariants, we give several new constraints of the set of smooth boundings of homology 3-spheres. As one of the corollaries, we give infinitely many homology 3-spheres which cannot bound any definite 4-manifold. As another corollary, we show that if the 1-surgery of a knot has negative Froyshov invariant, then the 1/n-surgeries (n>0) of the knot are linearly independent in the homology cobordism group. This is joint work with Yuta Nozaki and Kouki Sato.
November 17 Louis-Hadrien Robert (Luxembourg) Categorification of 1 and of the Alexander polynomial
November 24 Sarah Rasmussen (Cambridge) tba
December 1 Tao Li (Boston College) tba
December 8 Ciprian Manolescu (Stanford) tba
December 15 Siddhi Krishna (Georgia Tech) tba

The program is also contained in the RLGTS Google Calendar. To receive announcements by email, sign up to our mailing list.

Regensburg

Past talks in spring 2020

List of past talks in spring/summer 2020, with slides and videos

Zoom information

Zoom Meeting ID: 924 2829 6353

The password is the answer to the following riddle (lower case, singular, no article): As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold).

We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.

Organizers

Jonathan Bowden, Lukas Lewark, Raphael Zentner.