[Topology.beta] AG differential topology

[Rot, T.O. (Thomas)]

Dear all,

I'm sending this to the full topology mailing list because we will be reading a new paper and there might be renewed interest in this seminar. Further correspondence will not be send to this list so send me an email if you want to be included in this.

Tomorrow at 15:00 Ronen will speak about his own work on Polysymplectic things.

Then I'm on holiday.

We will commence the AG again in week 6 (of feb the 6th). My preference would be to not to move the AG. But I want to check if people still are able to attend on this timeslot. I also propose some other timeslots. Can you fill in this datumprikker if you want to attend?

https://datumprikker.nl/phxhgvy3cxt4k9u6

Just pretend that this is a generic week in the second semester.

I would like to read Thom's seminal work on manifolds up to cobordism " Quelques propriétés globales des variétés differentiables" for which he was awarded the Fields medal. I've attached an English translation of this paper.

In this paper Thom proves amongst other things

He proves that maps can be made transverse generically (This part I would like to skip as many of us know this already.)
He proves the Thom isomorphism
He shows that all classes in H_k(X;Z_2) are represented by the fundamental class a manifold mapping into X
He show that not all classes in H_k(X;Z) are represented by fundamental classes of manifolds mapping into X
He fully computes the unoriented cobordism ring.
He proves that two manifolds are cobordant iff they have the same Stiefel Whitney numbers

I think before we delve into this paper it would be good to study the Steenrod squares.

The plan is now:

In week 6 I will give an overview talk
In week 7 (maybe also 8) Michael (maybe someone else will do part II) will treat Steenrod squares following a book of Hausmann
After that we commence with the paper of Thom.

I will need volunteers for speakers. Send me an email if you want to talk.

Last thing: Two new talks in the DDT&G have been scheduled. See here: https://www.few.vu.nl/~trt800/ddtg.html . Please mark them in your agenda.

Best,
Thomas







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