IU/PU/IUPUI Joint Topology Seminar

April 25, 2015
IUPUI
Indianapolis, IN, USA

The 3rd meeting of the IU/PU/IUPUI Joint Topology Seminar will be held at IUPUI in Indianapolis, Indiana on Saturday April 25, 2015. Talks will begin at 10am and end at 12:30pm, followed by lunch.

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 McClure, Purdue University: The L-Homology Fundamental Class for IP-Spaces and the Stratified Novikov Conjecture
Carl McTague, Johns Hopkins University : Projective Planes and Bordism Rings

Schedule:

10am: Jim McClure

11:30am: Carl McTague

Abstracts:

Jim McClure, The L-Homology Fundamental Class for IP-Spaces and the Stratified Novikov Conjecture

Abstract: An IP-space is a pseudomanifold whose defining local properties imply that its middle perversity global intersection homology groups satisfy Poincaré duality integrally. The symmetric signature induces a map of Quinn spectra from IP bordism to the symmetric LL-spectrum of Z\mathbb{Z}.  Using this map, one can construct a fundamental LL -homology class for IP-spaces, and as a consequence prove the stratified Novikov conjecture for IP-spaces.


Carl McTague, Projective Planes and Bordism Rings

Abstract: There is a strong affinity between projective planes and bordism rings: (1) Every positive-dimensional element of the unoriented bordism ring is represented by an RP² bundle [Thom, Milnor, Stong]. (2) Every positive-dimensional element of the oriented bordism ring is represented by a CP² bundle [Milnor, Wall, Dold, Führing]. (3) Almost every element of the spin bordism ring is represented by an HP² bundle—precisely, the ideal of HP² bundles is the kernel of the Atiyah invariant [Anderson-Brown-Peterson, Kreck-Stolz]. This talk will focus on: (4) Almost every element of the string bordism ring is represented, at least up to powers of 2 and 3, by an OP² bundle—precisely, the ideal of OP² bundles is the kernel of the Witten genus, at least after inverting 6. This involves a pretty alignment of the arithmetic of binomial coefficients arising from Borel-Hirzebruch exceptional Lie group theoretic calculations and the Hovey-Ravenel-Wilson BP-Hopf-ring-theoretic calculation of string bordism at primes >3.

Directions

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:

January 31, 2015

November 8, 2014


Email: dramras at iupui dot edu