| Principal speaker | Robert Edwards, UCLA | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Title | Cantor groups, their classifying spaces, and their actions on ENR's
(An abstract may be found at the bottom of this announcement.) |
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| Professor Edwards will present 3 one-hour talks. In addition, participants are invited to give talks on their own research (approximately 20 minutes). | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Sponsored by the National Science Foundation and the University of Wisconsin - Milwaukee | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Schedule | The workshop will begin at 9:00 a.m. on Thursday June 10 in Engineering
and Mathematical Sciences (EMS) 495A with the first of three one hour lecture
by Professor Edwards. A continental breakfast will be provided in EMS 495B
beginning at 8:30 a.m. A nice map
of the UWM campus can be found on the UWM
Math Department web page.
For those arriving on Wednesday, an informal reception with snacks and beverages will be held in the Sandburg Residence Halls beginning at 7:00 pm. |
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| Transportation | Milwaukee has a major airport. Transportation between the airport and the campus will be provided. Instructions for approaching the campus by car and for parking are provided later. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Housing | A block of rooms has been reserved at Sandburg Hall on the UWM campus. Alternatively, fancier accommodations are available at the Astor Hotel downtown near the lake front and a short drive from campus. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Funding | Some funds are available to support the travel and living expenses of participants without other means of support. Graduate students are especially encouraged to apply. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Registration Fee | A $25 registration fee will be collected upon arrival. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Registration | If you plan to attend, please contact F. Ancel or C. Guilbault at the
addresses below by May 15. DEADLINE!!!
Include the following information.
1) Title of talk, if you would like to present one. 2) Estimate of uncovered expenses. 3) Flight information, if you are arriving by air. Register for Sandburg Hall housing directly. (See below.) For reservations at the Astor Hotel at the UWM rate contact Ancel or Guilbault. |
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| Addresses | Fredric D. Ancel
email: ancel@uwm.edu office phone: 414-229-5269 home phone: 414-352-7929 Craig R. Guilbault
Department of Mathematical Sciences
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| Sandburg Hall
Reservations |
Make these reservations directly either by calling Ken Busch at 414-229-4068
or by email at busch@aux.bfs.uwm.edu
. Give your name and address and indicate you are with the math conference.
He will send you registration information. Here are the room rates:
Single room - shared bath:
$27 per night
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| Organizers | F. Ancel and C. Guilbault, University of Wisconsin - Milwaukee
D. Garity, Oregon State University F. Tinsley, Colorado College D. Wright, Brigham Young University |
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| Participants |
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| Workshop Schedule | WEDNESDAY:
Informal reception in Sandburg Residence Halls beginning at 7:00 p.m. THURSDAY:
FRIDAY:
SATURDAY:
An outing will be planned for Saturday evening. Possibilities include: a Milwaukee Brewers baseball game, and the "Asian Moon Festival" at the Milwaukee lakefront. |
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| Driving instructions to UWM | If you are staying at the SANDBURG RESIDENCE HALLS, we suggest driving
directly there, parking in its underground lot, and walking to the sites
of the Workshop talks. The Workshop will be held in the ENGINEERING AND
MATHEMATICAL SCIENCES BUILDING (EMS), where parking is scarcer. Directions
for driving to and from the ASTOR HOTEL
are at the end of this description. These directions naturally pivot about LINCOLN MEMORIAL DRIVE, a scenic 3.5 mile drive along the Lake Michigan shore between downtown Milwaukee and the UWM campus. FROM SOUTH (Chicago or airport) TO LINCOLN MEMORIAL DR.: Take I94 west (it actually runs north) to Milwaukee. In downtown Milwaukee (7 miles north of the airport) take the I794 east exit. Take I794 east for 1 mile toward the lake and take the Lincoln Memorial Drive exit. Take Lincoln Memorial Drive north for 3.5 miles along the lake front. FROM WEST (Madison) TO LINCOLN MEM. DR.: Take I94 east to Milwaukee. In downtown Milwaukee take the I794 east exit. Take I794 east for 1 mile toward the lake and take the Lincoln Memorial Drive exit. Take Lincoln Memorial Drive north for 3.5 miles along the lake front. FROM LINCOLN MEM. DR. TO SANDBURG RESIDENCE HALLS: When Lincoln Memorial Drive curves west away from the lake and climbs a hill, get in the left lane. Proceed straight west through the traffic signal where Lincoln Mem. Dr. meets Lake Drive. (Here Lincoln Mem. Dr. becomes becomes Kenwood Blvd.) Proceed on Kenwood Blvd. through a 2nd traffic signal (Downer Ave.) and turn right (north) at the 3rd traffic signal Maryland Ave.). Take Maryland Ave. north for a long 1 and 1/2 blocks. Sandburg Halls are three towers on the right. Enter the underground parking lot just beyond the towers. After parking, find the registration desk on the main floor, where you can purchase a parking permit. FROM LINCOLN MEM. DR. TO ENGINEERING AND MATHEMATICAL SCIENCES BUILDING (EMS): Proceed as to Sandburg Halls, but once on Kenwood Blvd., go straight through the 3rd traffic signal (Maryland Ave.) and instead turn right (north) at the next corner (Cramer St.). Take Cramer north 1/2 block. EMS is the tower on the right. Parking near EMS may be scarce, though easier to find before 9AM. PARKING OPTION 1: Park in the underground lot beneath EMS which is entered from Cramer at the north end of EMS. Buy a permit from a machine in the lot. PARKING OPTION 2: Park in the surface lot at the corner of Cramer St. and Hartford Ave. The entrance to this lot is reached by proceeding north on Cramer to the next corner (Hartford Ave.), turning right (east), and turning into the first driveway on the right. Park in a space which does not require a Faculty/Staff Permit.Pay for parking at a machine in the lot. PARKING OPTION 3: Another surface lot is located on Kenwood next to the EMS building. Travelling west on Kenwood, enter the lot by turning right after Maryland Ave. but before Cramer. Park in a space which does not require a Faculty/Staff Permit. PARKING OPTION 4: There are 1- and 2-hour metered and unmetered parking places on the streets near EMS, the longer period parking places being found farther from EMS. FROM SOUTH (Chicago or airport) TO ASTOR HOTEL: Take I94 west (it actually runs north) to Milwaukee. At downtown interchange, take I43 north toward Green Bay. 3/4 of a mile north of the downtown interchange, take the "145, 4th St., Broadway" exit. Get in the right lane and take the Broadway exit. Take Broadway one block south to Juneau Ave. Turn left (east) on Juneau Ave. and take it 6 blocks east to the corner of Juneau and Astor St.. The hotel is on your left on the northwest corner. Park in front of the hotel and register in the lobby. You can park in the hotel lot for $3 a night, or find a place on the street. |
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ABSTRACT:
A cantor group is a topological group which is homeomorphic to the cantor set (i.e., is a second-countable infinite profinite group, if you wish). Basic examples are
1) any countably infinite direct product of nontrivial finite groups, and
2) the $p$-adic integers, for your favorite prime $p$.
The most significant open problem concerning cantor group actions is probably the:
Free-Set Z-Set (FSZS) Conjecture: Given any action by a cantor group on an ENR (= euclidean neighborhood retract), the free set of the action is a homology Z-set (in the ENR).
This can be regarded as a sort of Super Hilbert-Smith Conjecture, the HSC being the case where the ENR is a manifold.
In my talks I will present my work on this problem, including my solution (footnote: admittedly not yet verified by others), in the affirmative, of the free-action, finite-dimensional-quotient (= fdq) case, which is the natural case to consider first. After a brief introduction to cantor groups and their significance in locally compact topological group theory (Sample: Such a group is either a Lie group, or contains a cantor group (but not both!).), I'll discuss the (natural) classifying space(s) associated with free cantor group actions, pointing out along the way why the familiar principal-action (Milnor-type) classifying spaces are insufficient for general free actions. Then I'll describe their natural finite-dimensional (subclassifying space) ``skeleta,'' and how the free-fdq FSZS Conjecture follows if one can show that these skeleta are essential in some sense. Finally I'll outline my proof of the requisite essentiality. (It is reasonable to expect a manuscript to be available by then.)
The entrance exam for the 3-lecture-series has two problems:
I. Show that any cantor group embeds as a subgroup of a countable direct product group as in 1) above.
II. Show that a torsion-free cantor group contains as a subgroup the $p$-adic-integer group, for some $p$.
Additional problems will be supplied on request.
