# The Topology Seminar

## Spring 2008

**15th May: 13:15 - 15:00****, ****734, Sentralbygg II.**

Sarah Whitehouse (Sheffield): Infinite Sums of Adams Operations and Cobordism

**Abstract:** *We explain how to define an injective ring homomorphism from the ring of degree zero stable operations in p-local complex K-theory to the corresponding ring of complex cobordism perations. We show that the image of this map is precisely the centre of the target ring. This is joint work with Imma Galvez. I will also discuss some work in progress on a couple of different variants of this result, including an unstable one.*

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**28th April: 12:15 - 14:00****, ****734, Sentralbygg II.**

Marius Thaule: Open String Category II

**Abstract:** *I will pick up the thread from the previous seminar and finsih my description of the 2-category of open strings. I will also address issues raised concerning the R- and S-moves.*

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**21st April: 12:15 - 14:00****, ****734, Sentralbygg II.**

Marius Thaule: Open String Category

**Abstract:** *I aim to show the connection between the open-closed category of Baas, Cohen and Ramirez and the category of open strings.*

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**14th April: 13:15 - 14:00****, ****734, Sentralbygg II.**

Helge Maakestad: On Cohomology Operations and Characteristic Classes

**Abstract:** *I'll use tensor operations to define and prove elementary properties of characteristic classes with values in Grothendieck groups of fields, schemes and topological spaces. I'll calculate some examples and show that the characteristic classes of connections with values in Grothendieck groups of fields refine characteristic classes of connections with values in Chevalley-Hochschild cohomology. I'll also construct a characteristic class in the Grothendieck group of a Lie algebra of meromorphic vector fields associated to an arbitrary finite morphism of projective curves. This class is related to the ramification of the morphism.*

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**7th April: 12:15 - 14:00****, ****734, Sentralbygg II.**

Tore Kro: Stratified Spaces

**Abstract:** *I will review the notion of a Frölicher space. Next I will introduce the notion of a stratified space and give examples. For a point p in a stratified space W I will compute the germs of smooth curves at p in W and the continuous derivations at p in W. Moreover, I will show that any weak embedding if W into a Euclidean space has the structure of a Whitney stratified set. I will end the talk by comparing stratified spaces to Mather's abstract pre-stratified sets and to Kreck's stratifolds.*

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**27th February: 13:15 - 14:00****, ****734, Sentralbygg II.**

Tore Kro: The Classification of 2-Bundles

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**12th February: 10:15 - 12:00****, ****734, Sentralbygg II.**

Tore Kro: The Classifying Space of a Topological 2-Group

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**## Seminars given last semester