Department of Mathematics                           University of Haifa

Special Topology and Geometry Day

Wednesday, August 28, 2013

Room 614 of the Science & Education Building Univ. of Haifa

10:00-12:00   Emmanuel Farjoun  (Hebrew University of Jerusalem)

"On the cellular properties of nilpotent spaces"

13:00-13:50   Dr. Ajay Singh Thakur (University of Haifa):

"On trivialities of characteristic classes over suspension space"

14:00-14:50   Dr. Boris Chorny (University of Haifa at
Oranim):

"A classification of small homotopy functors from spectra to
spectra"

Abstracts are below, and also in the pdf file that can be accessed at
this url:
<http://www.math.technion.ac.il/~techm/temp/20130828Topo.pdf>

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Abstract:

10:00-12:00   Emmanuel Farjoun  (Hebrew University of Jerusalem)

"On the cellular properties of nilpotent spaces"

We will discuss new understanding of the cellularity and
homology/homotopy relations of nilpotent spaces. This implies some  new insights on
spaces with vanishing generalized (co)homology.

The problem starts with attempts the understand the fundamental group
of the cellular approximations of   K(\pi,1).

Similar problems in groups theory context and work of Flores and

Using a modified version of the classical Bousfield-Kan tower

and ideas stemming for Libman's thesis and work by Chacholski,

one can prove close homological and cellular relation between any
space  X and the tower   Z_sX

For nilpotent spaces this lead to a close relation between the
generalized  homology of X and that of its Postnikov approximations
P_nX,  formulated in the stronger terms of cellular inequality.

Finally, this provides an immediate algebraic formula for the
fundamental

group of any  cellular approximation of  BN for a general nilpotent

discrete group N.

Joint work with Wojciech Chacholski, Ramon  Flores, and Jerome
Scherer

Abstract

·        13:00-13:50   Dr. Ajay Singh Thakur (University of Haifa):

"On trivialities of characteristic classes over suspension space"

A CW-complex  X is said to be *W-trivial* if for any vector bundle
\xi over $X$, the total Stiefel-Whitney class  W(\xi)= 1.

It is a theorem of Atiyah-Hirzebruch that the k-fold suspension
\Sigma^k X

\ of any CW-complex X is W-trivial if k>8. It is therefore an
interesting question to understand for what value of  k, 0=< k =<8,
is the iterated suspension \Sigma^k X, of a CW-complex X,
W-trivial. A related notion is that of C-triviality. A CW-complex X
is said to be C-trivial if for any complex vector bundle \eta  over
X, the total Chern class  c(\eta)=1. In this talk we shall state some
general results and investigate  when the iterated suspensions of
projective spaces are W-trivial and C-trivial.

Abstract:

·        14:00-14:50   Dr. Boris Chorny (University of Haifa at
Oranim):

A classification of small homotopy functors from spectra to
spectra''

We show that every small homotopy functor from spectra to spectra is
weakly equivalent to a fi ltered colimit of representable functors
represented in co brant spectra. Moreover, we present this classi
cation as a Quillen equivalence of the category of small functors
from spectra to spectra equipped with the homotopy model structure
and the opposite of the pro-category of spectra with the strict model
structure.

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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il>
To see today's activities and other future and past activities go to
<http://www.math.technion.ac.il/~techm/today.html>
Announcement from: David Blanc   <BLANC@MATH.HAIFA.AC.IL>
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