Department of Mathematical Sciences > Research > Topology > Topology reading seminar
Welcome to the topology reading seminar!
Fall 2011: Surgery theory.
An outline of the programme is available here.
We meet on *Wednesdays at 10:15 in room 04.4.01*
| Sep 14 | Oscar Randal-Williams |
Smooth manifold techniques |
| Sep 21 |
Oscar Randal-Williams |
The h-cobordism theorem |
| Sep 28 |
Angela Klamt |
Poincare duality and Poincare complexes |
| Oct 5 |
Angela Klamt |
Poincare duality and Poincare complexes, II |
| Oct 12 |
Daniella Egas Santander |
Normal invariants and normal maps |
| Handout |
A Poincare complex inequivalent to a manifold |
|
| Oct 19 |
Oscar Randal-Williams |
Normal framed embeddings and immersions |
| Oct 26 |
Emanuele Dotto |
Surgery below the middle dimension |
| Nov 2 |
Ib Madsen |
The even-dimensional surgery obstruction |
| Nov 9 |
Ib Madsen |
The even-dimensional surgery obstruction, II |
| Nov 16 | Nathalie Wahl |
The odd-dimensional surgery non-obstruction |
| Nov 23 |
Anssi Lahtinen |
The surgery exact sequence |
| Nov 30 |
Oscar Randal-Williams |
Dimensions congruent to 2 modulo 4 |
| Dec 7 |
Oscar Randal-Williams |
Calculations |
References:
Algebraic and Geometric Surgery - Ranicki
Surgery on Compact Manifolds - Wall
Surgery on Simply Connected Manifolds - Browder
A Basic Introduction to Surgery Theory - Luck
Past seminars:
Fall 2010: Equivariant homotopy theory.
Here is a tentative outline . This document will be modified as we go along.
We meet on *Wednesdays at 10:15 in room 04.4.01*
| Sep 29 | Jesper Grodal |
Introduction |
| Oct 6 |
Richard Hepworth |
G-CW-complexes |
| Oct 13 | Alexander Berglund |
Elmendorf's Theorem |
| Oct 20 |
Oscar Randal-Williams |
Equivariant cohomology theories |
| Oct 27 |
Matthew Gelvin |
Smith theory |
| Nov 3 |
Toke Nørgård-Sørensen |
Self maps of a representation sphere |
| Nov 10 |
Bob Oliver |
Self maps of a representation sphere II |
| Nov 17 |
Samik Basu |
G-equivariant stable homotopy theory |
| Nov 24 |
Samik Basu |
G-equivariant stable homotopy theory (cont.) |
| Dec 1 |
Anssi Lahtinen |
The Atiyah-Segal completion theorem |
| Dec 8 |
Otgonbayar Uuye |
Restriction maps in equivariant K-theory |
| Dec 15 |
- |
- |
| Jan 12 |
Oscar Randal-Williams |
The calculation BU^hZ/2 = BO. |
| Jan 19 | Anssi Lahtinen |
Change of groups and duality theory |
| Jan 26 |
Richard Hepworth | Mackey functors |
References:
Adams, Prerequisites (on equivariant stable homotopy) for Carlsson's
lecture.
Algebraic topology, Aarhus 1982 (Aarhus, 1982),
483-532,
Lecture Notes in Math., 1051, Springer, Berlin, 1984.
Greenlees-May, Equivariant stable homotopy theory
Handbook of algebraic topology, 277-323, North-Holland, 1995.
Elmendorf, Systems of fixed point sets ,
Trans. Amer. Math. Soc. 277 (1983), no. 1, 275-284.
Hill-Hopkins-Ravenel,
On the non-existence of elements of Kervaire invariant one
arXiv:0908.3724v1 [math.AT]
Mandell-May,
Equivariant Orthogonal Spectra and S-modules
Mem. Amer. Math. Soc. 159 (2002), no. 755.
May, Equivariant homotopy and cohomology theory, CBMS Regional Conference Series in Mathematics, 91.
McClure, Restriction maps in equivariant K-theory , Topology Vol. 25, No. 4,pp. 399 - 409, (1986).
Spring 2010:
We meet on
*Tuesdays at 14:15 and Fridays at 13:15 in room 04.4.01*
| Feb 3 | David Ayala, |
Derived Koszul Duality in the Algebraic K-Theory of Spaces [BM2] |
| Feb 5 |
David Ayala, |
Derived Koszul Duality in the Algebraic K-Theory of Spaces II [BM2] |
| Feb 9 | Richard Hepworth, | Derived Koszul Duality in the Algebraic K-Theory of Spaces III [BM2] |
| Feb 23 | Andrew Blumberg | The S.'-construction [BM1] |
| Mar 2 |
Richard Hepworth | The Blob Complex I |
| Mar 5 |
Richard Hepworth | The Blob Complex II |
| Mar 9 |
Pascal Lambrechts |
The Goodwillie embedding calculus I |
| Mar 12 |
Pascal Lambrechts |
The Goodwillie embedding calculus II |
| Mar 16 |
David Ayala | Very Poincaré duality I [DWW, L] |
| Mar 19 |
David Ayala | Very Poincaré duality II [DWW, L] |
| Mar 23 |
Samik Basu |
A cellular nerve for higher categories I [B] |
| Mar 26 |
Samik Basu |
A cellular nerve for higher categories II [B] |
| Mar 30 |
Samik Basu |
A cellular nerve for higher categories III [B] |
| Apr 9 |
Richard Hepworth | Iterated wreath products and iterated loop spaces I [B2] |
| Apr 13 |
Richard Hepworth |
Iterated wreath products and iterated loop spaces II [B2] |
| Apr 16 |
Richard Hepworth | Iterated wreath products and iterated loop spaces III [B2] |
| Apr 21 |
Richard Hepworth |
Iterated wreath products and iterated loop spaces IV [B2] |
| Apr 23 |
Samik Basu |
Iterated wreath products and iterated loop spaces V [B2] |
| Apr 28 |
Pascal Lambrechts | Iterated wreath products and iterated loop spaces VI [B2] |
| May 5 |
Alexander Berglund |
The Barratt-Eccles operad I [BE, B3] |
| May 7 | Alexander Berglund |
The Barratt-Eccles operad II [BE, B3] |
| May 18 |
Richard Hepworth |
The additivity theorem [BV], [D] |
| May 21 |
Ib Madsen |
Homology operations |
| Jun 1 |
Otgonbayar Uuye |
Homotopical Algebra for C^*-algebras |
References:
[BE] M.G. Barratt, P.J. Eccles, Gamma^+-structures I, II, III, Topology, Vol. 13, (1974), 25-45, 113-126, 199-207.
[B] C. Berger, A cellular nerve for higher categories, Adv. Math. 169 (2002), no. 1, 118-175.
[B2] C. Berger , Iterated wreath product of the simplex category and iterated loop spaces, Adv. Math. 213 (2007), no. 1, 230-270.
[B3] C. Berger, Combinatorial models for real configuration spaces and E_n-operads.
[BM1] A. Blumberg, M. Mandell, The localization sequence for the algebraic K-theory of topological K-theory, Acta Math., 200 (2008), 155-179.
[BM2] A. Blumberg, M. Mandell, Derived Koszul Duality and Involutions in the Algebraic K-Theory of Spaces, arXiv:0912.1670v1 [math.KT]
[BV] J.M. Boardman, R.M. Vogt, Homotopy Invariant Algebraic Structures on Topological Spaces, Lecture notes in Math. 347 (1973).
[D] G. Dunn, Tensor product of operads and iterated loop spaces, J. Pure. Appl. Algebra 50 (1988), 237 - 258.
[DWW] W. Dwyer, M. Weiss, B. Williams, A parametrized index theorem for the algebraic K-theory Euler class. Acta Math. 190 (2003), no. 1, 1-104.
[L] J. Lurie, Derived algebraic geometry VI: E_k algebra, arXiv:0911.0018v1 [math.AT]
Fall 2009:
This semester (Fall 2009) we are reading the paper
F. Waldhausen, Algebraic K-theory of spaces,
Lecture Notes in Math. 1126, 1985, pp. 318-419
The paper is available at here.
We meet twice a week and go through a part of the paper together. As a platform for discussions, someone presents the material to the others in an informal talk. This task circulates among volunteers.
| Sep 30 |
Alexander Berglund | Categories with cofibrations and weak equivalences | |
| Oct 7 |
Alexander Berglund |
S_n C as a Waldhausen category | |
| Oct 14 |
David Ayala |
The additivity theorem |
|
| Oct 21 |
David Ayala |
The additivity theorem (continued) | |
| Oct 23 |
David Ayala | Thomason's interpretation. E(A,C,B) as a Waldhausen cat. | |
| Oct 28 |
David Ayala | The additivity theorem (continued) |
|
| Oct 30 | - |
- |
|
| Nov 4 |
Ib Madsen |
Duality and the S.-construction | |
| Nov 6 | - |
- |
|
| Nov 11 | Otgonbayar Uuye | Relative K-theory and cofinality |
|
| Nov 13 |
Otgonbayar Uuye | Relative K-theory and cofinality (continued) | |
| Nov 18 |
Ib Madsen | Duality and the S.-construction II |
|
| Nov 20 |
- |
- |
|
| Nov 25 | Alexander Berglund |
Cylinder functors and the fibration theorem. |
|
| Nov 27 |
Alexander Berglund | Cylinder functors and the fibration theorem (continued) |
|
| Dec 2 |
Samik Basu |
The approximation theorem. | |
| Dec 4 |
Samik Basu |
The approximation theorem (continued) | |
| Dec 9 |
David Ayala | Definition of A(X) |
|
| Dec 11 |
David Ayala |
Definition of A(X) (continued) |
|
| Dec 16 |
Alexander Berglund |
Waldhausen's S.-construction vs. Quillen's Q-construction |
Last year's seminar was about symmetric spectra.