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University of Cambridge > Talks.cam > Junior Geometry Seminar > The discrete bordism category in dimension 1

## The discrete bordism category in dimension 1Add to your list(s) Download to your calendar using vCal - Jan Steinebrunner (Oxford)
- Friday 18 October 2019, 16:00-17:00
- MR13.
If you have a question about this talk, please contact Nils Prigge. The discrete bordism category hCob_d has as objects closed (d-1)-manifolds and as morphisms diffeomorphism classes of d-dimensional bordisms. This is a simplified version of the topologically enriched bordism category Cob_d whose classifying space B(Cob_d) been completely determined by Galatius-Madsen-Tillmann-Weiss in 2006. In comparison, little is known about the classifying space B(hCob_d). I will identify B(hCob_1) as a circle bundle over a delooping of BCob_2, showing, in particular, that the rational cohomology ring of hCob_1 is polynomial on classes \kappa_i in degrees 2i+2 for all i>=1. The seemingly simpler category hCob_1 hence has a more complicated classifying space than Cob_1. Moreover, I will give combinatorial formulas for cocycles on hCob_1 that represent \kappa_i. This talk is part of the Junior Geometry Seminar series. ## This talk is included in these lists:- All CMS events
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