Seifert surfaces for virtual knots
Organizers
Vassily Manturov
, Shiquan Ren
,
Zhe Yan Wan
Speaker
Eiji Ogasa
Time
Wednesday, July 31, 2024 3:30 PM - 5:00 PM
Venue
A3-2-301
Online
Zoom 831 5020 0580
(141592)
Abstract
We introduce Seifert surfaces for virtual knots.
Virtual knots are represented by knots in thickened oriented surfaces,
which may be a non-zero cycle. Although it may be a non-zero cycle,
we can define Seifert surfaces for virtual knots.
We also define Seifert matrices associated with our new Seifert surfaces.
Furthermore, by using our new Seifert matrices,
we introduce the Alexander polynomials and the signature.
Our Alexander polynomial of virtual knots can obstruct from being classical knots.It is mirror sensitive as isotopy invariants.
Our signature is mirror sensitive as diffeomorphic invariants.
This talk is based on the paper,
New invariants for virtual knots via spanning surfaces
Journal of knot theory and its ramifications 2024 arXiv:2207.08129 [math.GT]
written by András Juhász, Louis H. Kauffman, and the speaker.
Virtual knots are represented by knots in thickened oriented surfaces,
which may be a non-zero cycle. Although it may be a non-zero cycle,
we can define Seifert surfaces for virtual knots.
We also define Seifert matrices associated with our new Seifert surfaces.
Furthermore, by using our new Seifert matrices,
we introduce the Alexander polynomials and the signature.
Our Alexander polynomial of virtual knots can obstruct from being classical knots.It is mirror sensitive as isotopy invariants.
Our signature is mirror sensitive as diffeomorphic invariants.
This talk is based on the paper,
New invariants for virtual knots via spanning surfaces
Journal of knot theory and its ramifications 2024 arXiv:2207.08129 [math.GT]
written by András Juhász, Louis H. Kauffman, and the speaker.