Topology Seminars 2011/12

• 6 February
  2012 Equivariant Bordism and Labelled Graphs
  Alastair Darby (University of Manchester)
  
  3pm in FRANK ADAMS 2
  Abstract (click to view)

  Results of GKM-theory show that the equivariant cohomology, and other important topological information, of a large class of manifolds with torus action can be combinatorially encoded in a regular labelled graph. We will look at how this may be mimicked in geometric equivariant bordism. We will begin by looking at manifolds with a real torus action and if time permits move on to the more compl icated case of unitary toric manifolds.

• 13 February
  2012 The Kervaire invariant
  John Jones (University of Warwick)
  
  3pm in FRANK ADAMS 2
  Abstract (click to view)

  In 2009 Mike Hill, Mike Hopkins and Doug Ravenel proved that the only dimensions in which there are framed manifolds with Kervaire invariant one are 2, 6, 14, 3 0, 62 and possibly 126. In this talk I will try to highlight the significance o f this result for both differential topology and homotopy theory and summarise w hat is known in the 6 special dimensions.

• 20 February
  2012 Classification of complex projective towers up to dimension 8 and cohomological rigidity.
  Shintaro Kuroki (Osaka City University Advanced Mathematical Institute)
  
  3pm in FRANK ADAMS 2
  Abstract (click to view)

• 27 February
  2012 Infrasolv real moment-angle manifolds and small covers.
  Shintaro Kuroki (Osaka City University Advanced Mathematical Institute)
  
  3pm in FRANK ADAMS
  Abstract (click to view)

• 5 March
  2012 No seminar: President and Vice Chancellor, Professor Dame Nancy Rothwell's visit
  
  
  3pm in FRANK ADAMS 2
  Abstract (click to view)

• 12 March
  2012 Almost complex structures for quasi toric manifolds
  Dietrich Notbohm (VU Amsterdam)
  
  3pm in FRANK ADAMS 2
  Abstract (click to view)

  Quasi toric manifolds are the topological version of smooth toric varieties, but in general do not carry a complex structure. The next what you can hope for is whether their tangent bundles can be given the structure of a complex vector b undle. We will discuss this question in the equivariant case, i..e. with respect to the associated torus action .

• 19 March
  2012 n-fold groupoids, n-types and n-track categories
  Simona Paoli (University of Leicester)
  
  3pm in FRANK ADAMS 2
  Abstract (click to view)

  Most homotopy invariants of topological spaces are filtered by dimension, so it is useful to have finite dimensional approximations to homotopy theories. We de scribe an algebraic model for the latter, which we call n-track categories. An a ppropriate algebraic model of n-types is developed for this purpose, with what w e call n-typical n-fold groupoids. These lead to an explicit connection between n-types and iterated loop spaces and exhibit other useful properties. This is jo int work with David Blanc.

• 16 April
  2012 Hopf algebras in Topology and Algebra
  Martin Crossley (Swansea University)
  
  3pm in FRANK ADAMS 2
  Abstract (click to view)

• 23 April
  2012 Double point surfaces of immersions 2
  Peter Eccles (University of Manchester)
  
  3pm in FRANK ADAMS 2
  Abstract (click to view)

  Given a self-transverse immersion of a closed smooth manifold M of dimension n-k in a smooth manifold N of dimension n, the r-fold intersection set is the image of an immersion of a closed manifold of dimension n-rk. In a previous talk on 17 October I described a general method for determining the bordism class of the r-fold intersection manifold (in the case when N is Euclidean space) from the H urewicz image of the element in the stable homotopy of MO(k) represented by the immersion. In this talk I will review this result and describe how applying it in the case when r = 2 and n-2k = 2 enables us to determine the dimensions for w hich the double point surface of an immersion in Euclidean space can be a non-bo undary (joint work with Mohammad Asadi). I will then go on (possibly in a subse quent talk) to discuss how these methods can be extended to immersions in more g eneral manifolds, considering in particular immersions in complex projective spa ce (joint work with Azzh Al-Shehry).

• 30 April
  2012 no seminar today
  
  
  3pm in FRANK ADAMS 2
  Abstract (click to view)

Further information

For further information please contact Jelena Grbić, the seminar organiser.