xf IU/PU/IUPUI Joint Topology Seminar

IU/PU/IUPUI Joint Topology Seminar

January 31, 2015
IUPUI
Indianapolis, IN, USA

The 2nd meeting of the IU/PU/IUPUI Joint Topology Seminar will be held at IUPUI in Indianapolis, Indiana on Saturday January 31, 2015. Talks will begin at 10am and end at 12:30pm, and we plan to go to lunch afterwards.

Registration

If you plan to attend, please email Dan Ramras (dramras at iupui.edu), and indicate if you will need a parking pass and if you plan to come to lunch. We can provide parking passes, which allow you to park in the lots in front of the LD building. (Most parking spots on the IUPUI campus require a permit, even on weekends.) Note that IU parking permits are valid at IUPUI, but Purdue permits are not. More details are below.

Confirmed Speakers

Jim Davis, Indiana University: Bordism of $L^2$ -bettiless manifolds

Bert Guillou, University of Kentucky: Eta and the structure of motivic Ext

Schedule:

10am: Jim Davis

11:30am: Bert Guillou

Abstracts:

Bert Guillou, Eta and the structure of motivic Ext

Abstract: Let A denote the motivic Steenrod algebra. The motivic Adams spectral sequence has E₂ term given by Ext_Aand converges to the motivic stable homotopy groups of spheres. The motivic Hopf map eta is not nilpotent, contrary to the classical case, and this is represented by an infinite h₁-tower in Ext_A. I will discuss the h₁-local portion of Ext_A, which computes the homotopy of the

$\eta

-local motivic sphere. We will also see that the h₁-towers give the only classes appearing above the classical Adams vanishing line. This is joint work with Dan Isaksen.

Jim Davis, Bordism of $L^2$ -bettiless manifolds

Abstract: A manifold is $L^2$ -bettiless if all of its $L^2$ -betti numbers vanish. (It is also called anharmonic since there are no nontrivial $L^{2}$ -harmonic forms.) For a manifold with fundamental group $\mathbb{Z}^n$ , a manifold is $L^2$ -bettiless if and only if it is acyclic with $\mathbb{Q}(t_1, \dots, t_n)$ -local coefficients. We are interested in $\Omega^{(2)}_n(BG)$ , oriented bordism of $L^2$ -bettiless manifolds with respect to a regular $G$ -cover.

Theorem: There is a long exact sequence
$\cdots \to \Omega^{(2)}_k(B\mathbb{Z}^n) \to \Omega_k(B\mathbb{Z}^n) \to L_k(\mathbb{Q}(t_1, \dots, t_n)) \to \cdots$
Furthermore these $L$ -groups vanish for $k$ not divisible by 4.

This is proven by modifying the surgery program with a few tricks. Interesting connections with Witt groups of hermitian forms will be discussed, as well as generalizations to virtually abelian groups.

This is joint work with Sylvain Cappell and Shmuel Weinberger.

Directions

All talks will be held in LD 026 (basement of the math building) on the IUPUI campus in downtown Indianapolis. Note that the LD building and the SL building are joined; LD rooms are on the southern side (further from Michigan St.).

Parking Information

IU permits are valid in certain IUPUI surface lots. Detailed information is available here. There are two lots in front of the LD/SL building. Those with an IU A or C permit can park in either lot, and those with an IU E permit can park in the southern lot. Purdue permits are not honored at IUPUI. If you will need a parking pass, please email Dan Ramras (dramras at iupui.edu).

Campus Map

Organizers

Dan Ramras (dramras at iupui dot edu)
Mike Mandell (mmandell at indiana dot edu)
David Gepner (dgepner at purdue dot edu)

Please contact us with questions.

Past meetings:

November 8, 2014

Email: dramras at iupui dot edu