Topology Seminar - OSU
http://www.math.osu.edu/~fowler/teaching/
Topology Seminar at the Ohio State University
en-usCopyright 2010 Jim Fowlerfowler@math.osu.edu (Jim Fowler)Thu, 02 Oct 2014 14:07:30 -040060Dan Burghelea: Refinements of Betti numbers
http://www.math.osu.edu/~fowler/topology/index.html#2014-10-07T15:00:00+00:00
http://www.math.osu.edu/~fowler/topology/index.html#2014-10-07T15:00:00+00:00Dan Burghelea (The Ohio State University): Refinements of Betti numbers.
In this talk I will propose a refinement of the Betti numbers provided by a continuous real valued map. These refinements consist of monic polynomials in one variable with complex coefficients, of degree the Betti numbers. A number of remarkable properties of these polynomials will be discussed.\nIn case X is a Riemannian manifold these refinements can be even "more refined"; One can assign to the map and each nonnegative integer a collection of mutually orthogonal subspaces of the Harmonic forms = deRham cohomology in degree labelled by the zeros of the above mentioned polynomials and of dimension the multiplicity of the corresponding zero.\nIf the map is a Morse function the polynomials can be calculated in terms of critical values of the map and the number of trajectories of the gradient of the Morse function between critical points.
Tue, 07 Oct 2014 15:00:00 +0000Michael Donovan: TBA
http://www.math.osu.edu/~fowler/topology/index.html#2014-10-14T15:00:00+00:00
http://www.math.osu.edu/~fowler/topology/index.html#2014-10-14T15:00:00+00:00Michael Donovan (MIT): TBA.
TBA
Tue, 14 Oct 2014 15:00:00 +0000Kun Wang: Some structural results for Farrell's twisted Nil-groups
http://www.math.osu.edu/~fowler/topology/index.html#2014-10-16T15:00:00+00:00
http://www.math.osu.edu/~fowler/topology/index.html#2014-10-16T15:00:00+00:00Kun Wang (Vanderbilt University): Some structural results for Farrell's twisted Nil-groups.
Farrell Nil-groups are generalizations of Bass Nil-groups to the twisted case. They mainly play role in (1) The twisted version of the Fundamental theorem of algebraic K-Theory (2) Algebraic K-theory of group rings of virtually cyclic groups (3) as the obstruction to reduce the family of virtually cyclic groups used in the Farrell-Jones conjecture to the family of finite groups. These groups are quite mysterious. Farrell proved in 1977 that Bass Nil-groups are either trivial or infinitely generated in lower dimensions. Recently, we extended Farrellâ€™s result to the twisted case in all dimensions. We indeed derived some structural results for general Farrell Nil-groups. As a consequence, a structure theorem for an important class of Farrell Nil-groups is obtained. This is a joint work with Jean Lafont and Stratos Prassidis.
Thu, 16 Oct 2014 15:00:00 +0000Nick Gurski: TBA
http://www.math.osu.edu/~fowler/topology/index.html#2014-10-21T15:00:00+00:00
http://www.math.osu.edu/~fowler/topology/index.html#2014-10-21T15:00:00+00:00Nick Gurski (University of Sheffield): TBA.
TBA
Tue, 21 Oct 2014 15:00:00 +0000Michael Ching: TBA
http://www.math.osu.edu/~fowler/topology/index.html#2014-10-28T15:00:00+00:00
http://www.math.osu.edu/~fowler/topology/index.html#2014-10-28T15:00:00+00:00Michael Ching (Amherst College): TBA.
TBA
Tue, 28 Oct 2014 15:00:00 +0000Michael Andrews: TBA
http://www.math.osu.edu/~fowler/topology/index.html#2014-11-04T15:00:00+00:00
http://www.math.osu.edu/~fowler/topology/index.html#2014-11-04T15:00:00+00:00Michael Andrews (MIT): TBA.
TBA
Tue, 04 Nov 2014 15:00:00 +0000Luis A. Pereira: TBA
http://www.math.osu.edu/~fowler/topology/index.html#2014-11-18T15:00:00+00:00
http://www.math.osu.edu/~fowler/topology/index.html#2014-11-18T15:00:00+00:00Luis A. Pereira (University of Virginia): TBA.
TBA
Tue, 18 Nov 2014 15:00:00 +0000Jon Beardsley: Ravenel's $X(n)$ Spectra as Iterated Hopf-Galois Extensions
http://www.math.osu.edu/~fowler/topology/index.html#2014-11-25T15:00:00+00:00
http://www.math.osu.edu/~fowler/topology/index.html#2014-11-25T15:00:00+00:00Jon Beardsley (Johns Hopkins University): Ravenel's $X(n)$ Spectra as Iterated Hopf-Galois Extensions.
We prove that the X(n) spectra, used in the proof of Ravenel's Nilpotence Conjecture, can be constructed as iterated Hopf-Galois extensions of the sphere spectrum by loop spaces of odd dimensional spheres. We hope to leverage this structure to obtain a better understanding of the Nilpotence Theorem as well as develop an obstruction theory for the construction of complex orientations of homotopy commutative ring spectra. The method of proof is easily generalized to show that other Thom spectra can be considered intermediate Hopf-Galois extensions, for instance the fact that MU is a Hopf-Galois extension of MSU by infinite dimensional complex projective space.
Tue, 25 Nov 2014 15:00:00 +0000Yilong Wang: TBA
http://www.math.osu.edu/~fowler/topology/index.html#2014-12-02T15:00:00+00:00
http://www.math.osu.edu/~fowler/topology/index.html#2014-12-02T15:00:00+00:00Yilong Wang (The Ohio State University): TBA.
TBA
Tue, 02 Dec 2014 15:00:00 +0000Gabriel Valenzuela: TBA
http://www.math.osu.edu/~fowler/topology/index.html#2014-12-09T15:00:00+00:00
http://www.math.osu.edu/~fowler/topology/index.html#2014-12-09T15:00:00+00:00Gabriel Valenzuela (Wesleyan University): TBA.
TBA
Tue, 09 Dec 2014 15:00:00 +0000