dc.contributor.author Litvanyi, Peter Ivo dc.date.accessioned 2018-08-08T02:11:41Z dc.date.available 2018-08-08T02:11:41Z dc.date.issued 1993 dc.identifier.uri http://hdl.handle.net/11122/9385 dc.description Thesis (Ph.D.) University of Alaska Fairbanks, 1993 dc.description.abstract Commutators between the transfer and Steenrod squares have been investigated by several authors. Let X be a finite simplicial complex and $\tau$ be a regular involution on X. If $\tau$ has no fixed point, then the commutator is trivial by certain results in generalized cohomology theory. For involutions with possible fixed points, the commutator was first expressed by Bott as $\Delta\sp*$Sq$\sp{\rm i}$ + Sq$\sp{\rm i}\Delta\sp* = \mu$Sq$\sp{\rm i-1}\Delta\sp*.$ Here $\Delta\sp*$ is the transfer map and $\mu$ denotes the connecting morphism of the Smith sequence. Another formula, closely related to the one above, was given by Kubelka and gives the commutator in terms of the cohomology class restricted to the fixed point set and certain characteristic classes arising from the double cover of the complement to the fixed point set. In this thesis, I prove the generalization of the formulas above for sheaf cohomology. As one of the consequences, due to the powerful nature of sheaf theory we gain the results without serious restrictions on the space: X is required to be paracompact, Hausdorff. In Chapter 1, I review the standard sheaf-theoretical constructions for both the transfer and the Steenrod powers based on Bredon's results. I state and prove a few technical lemmas on Smith sequences that are necessary in my setting. In Chapter 2, I state and prove the analogue of Bott's formula for paracompact Hausdorff spaces. In Chapter 3, we derive a generalization of Kubelka's formula for spaces as above. dc.subject Mathematics dc.title Transfer and Steenrod squares dc.type Thesis dc.type.degree phd dc.contributor.chair Piacenza, Robert refterms.dateFOA 2020-03-06T01:17:49Z
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