The 38th Cascade Topology Seminar will be held at Portland State University on Saturday October 28 and Sunday October 29th. All talks will be in Neuberger Hall, NH 350.

Speakers, Titles, and Abstracts:

• Laura Scull, University of British Columbia
  Symmetry and fundamental groups
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    Introducing symmetries of spaces leads to generalizations of the fundamental group designed to encode this extra structure. Equivariant homotopy theorists have defined an 'equivariant fundamental groupoid' using some category theory. Fundamental groups have also been defined for orbifolds and stacks, which possess local symmetry structure. Although the definitions in these cases are very different, the results can be strikingly similar. I will discuss the different approaches and some work in progress (that is, somewhat speculative) in relating them.

• Genevieve Walsh, University of Quebec at Montreal
  Commensurability classes of 2-bridge knots
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    Two 3-manifolds are said to be commensurable if they have a common finite-sheeted cover. Commensurability classes are a reasonable way to organize hyperbolic 3-manifolds. For example, if a manifold is virtually fibered or virtually Haken, then so is every manifold in its commensurability class. However, the general problem of determining if two hyperbolic 3-manifolds are commensurable is difficult. We show that a hyperbolic 2-bridge knot complement is the unique knot complement (in S^3) in its commensurability class. The proof relies heavily on facts particular to 2-bridge knots.

    There are commensurability classes that contain more than one hyperbolic knot complement. For example, this can happen if one of the knots admits a lens space surgery. We speculate on the general case.

    This is joint work with Alan Reid.

• Jessica Purcell, University of Texas at Austin
  Links with reflective symmetry
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    Abstract: We discuss a class of links for which we can determine a great deal of geometric information given only a diagram of the link. Since any knot is obtained by Dehn filling such a link, we discuss applications to questions on Dehn filling and the geometry of knot complements.

• Thomas Mattman, University of California-Chico
  Boundary slopes (nearly) bound cyclic slopes
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    Abstract: Let $r_m$ and $r_M$ be the least and greatest finite boundary slopes of a hyperbolic knot $K$ in $S^3$. We show that any cyclic surgery slopes of $K$ must lie in the interval ${[} r_m - 1/2, r_M + 1/2 {]}$.

• John Radcliffe, Vanderbilt University
  Some examples of aspherical 4-manifolds that are homology 4-spheres
  Authors: John Ratcliffe and Steven Tschantz
  Speaker: John Ratcliffe
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    Abstract: In this talk I will describe the construction of infinitely many homotopy types of aspherical 4-manifolds that are homology 4-spheres. This construction solves Problem 4.17 on Kirby's problem list.

Location and Lodging:

• Campus Map
• Getting Around (directions, parking, transportation ...)

Portland State University is located on the south end of downtown Portland. Portland has many fine hotels conviniently located near the PSU Campus. Participants are recommended to University Place, just four blocks from the meeting site, or to the Mark Spencer Hotel, a 5 minute streetcar ride from the meeting site. More budget accommodations can be found at the Portland Days Inn-City Center, a 6 block walk to the meeting site.

Travel Support:

The Cascade Topology Seminar is supported in part by grants from the National Science Foundation, the Pacific Institute for the Mathematical Sciences, and is a Mathematical Sciences Research Institute MER Network Conference. The support of these agencies is gratefully acknowledged. The Seminar has dedicated funding available to support the participation of graduate students, early career mathematicians, and members of traditionally underrepresented groups. Members of these aforementioned groups are especially encouraged to apply and attend.