[Binghamton Geometry/Topology Seminar] October 4 and 7 (TWO TALKS)

[Lucas Sabalka]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

For this upcoming week, the Geometry and Topology Seminar will have two
speakers, one on Monday and one on Thursday.  On Monday, Jim Davis will
speak at 5:00, and on Thursday Brita Nucinkis will speak at the usual time.
Both talks will be in the usual room, LN 2205, followed by coffee/tea in the
Anderson Reading Room.  Titles and abstracts are below.


Monday 4 October, 5:00-6:00pm

Jim Davis (Indiana U)

Title:  Equivariant rigidity, Smith theory, and actions on tori

Abstract: I will state the problem of equivariant rigidity for a discrete
group G. A complete analysis will be made for crystallographic group G_n
given by the semidirect product of Z/2 acting on Z^n by multiplication by
-1. I will discuss the theorem that G_n satisfies equivariant rigidity when
n is congruent to 0 or 1 modulo 4 and the constructions of counterexamples
when n > 3 is congruent to 2 or 3 modulo 4. Equivalently, one classifies
involutions on tori which induce multiplication by -1 on the first homology.
Ingredients are Smith theory, surgery theory, and the Farrell-Jones
conjecture. A key aspect of the application of Smith theory is the use of a
theorem from point-set topology that a connected complete metric space is
path-connected. This is joint work with Qayum Khan and Frank Connolly.


Thursday, 7 October 2:50-3:50pm

Brita Nucinkis (University of Southampton)

Title:  Fixed Points of Finite Groups Acting on Generalized Thompson Groups

Abstract: Joint work with D.H. Kochloukova and C. Martinez-Perez. In this
talk I will discuss cohomological finiteness conditions of centralisers of
finite order automorphisms of the generalised Thompson groups $F_{n,\infty}$
well as conjugacy classes of finite subgroups in finite extensions of
$F_{n,\infty}$. In particular, it turns out that centralisers of finite
automorphisms in $F_{n,\infty}$ are either of type FP_{\infty}$ or not
finitely generated. This has implications on the type of the classifying
space for proper actions EG of finite extensions of $F_{n,\infty}$: Any
finite extension $G$ of $F_{n,\infty}$, where the elements of finite order
act on $F_{n,\infty}$ via conjugation with piecewise-linear homeomorphisms,
admits a finite type model for EG. In particular, finite extensions $G$ of
$F = $F_{2,\infty}$ admit a finite type model for EG.
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