Homotopy Properties of the Poset of Nontrivial p-Subgroups of a Group – University of Copenhagen

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Department of Mathematical Sciences > Research > Topology, Functional Analysis and Algebra > Topology > Subgroup Complexes

This is the webpage for our reading seminar on Quillen's paper [Quillen].  The first meeting will take place on Tuesday 25 Feb 2014 at 13:15 in the seminar room on the 4th floor.

Talks.

25 Feb 2014 13-15

Introduction

1. The Simplicial Complex Associated with a Poset

Markus Szymik

3 Mar 2014 10-12

2. The Posets S_p(G) and A_p(G)

3. Relation to Buildings

Dieter Degrijse

4 Mar 2014 13-15

4. Euler characteristic of S_p(G)

Tomasz Prytula

Kristian Moi

6 Mar 2014 10-12

5. Connected components

6. Relation with Alperin's Fusion Theorem

Isabelle Laude

7 Mar 2014 14-16

Around Quillen's Conjecture

Jesper M. Møller

10 Mar 2014 10-12

7. Local Systems and Homology

Irakli Patchkoria

11 Mar 2014 13-15

8. Spherical and Cohen-Macaulay Posets

9. Spherical and Cohen-Macaulay Posets (Continued)

Markus Szymik

13 Mar 2014 10-12

10. The CM Property for A_p(G)

11. Extensions by Certain Solvable Groups

Sune P. Reeh

14 Mar 2014 14-16

12. Applications

John Foley

References.

[Gelvin+Møller] M. Gelvin, J.M. Møller. Homotopy equivalences between p-subgroup categories. Preprint. (link)

[Grodal] J. Grodal. Higher limits via subgroup complexes. Ann. of Math. 155 (2002) 405-457.

[Grodal+Smith] J. Grodal, S.D. Smith. Propagating sharp group homology decompositions. Adv. Math. 200 (2006) 525-538.

[Jacobsen+Møller] M.W. Jacobsen, J. M. Møller. Euler characteristics and Möbius algebras of p-subgroup categories. J. Pure Appl. Algebra 216 (2012) 2665-2696.

[Quillen] D. Quillen. Homotopy properties of the poset of nontrivial p-subgroups of a group. Adv. in Math. 28 (1978) 101-128.

[Reeh] S.P. Reeh. Homotopiteori for pomængden af p-undergrupper i en endelig gruppe. Master's Project. (link)