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Computations in Twisted Morava K-theory

Yarosh, Aliaksandra (2017) Computations in Twisted Morava K-theory. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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In this dissertation we compute twisted Morava K-theory of all connective covers of the stable orthogonal group and stable unitary group, their classifying spaces, as well as spheres and Eilenberg-MacLane spaces. We employ techniques from [SW15] such as the universal coefficient theorem and Atiyah-Hirzebruch spectral sequence, and develop a similar theory for twists by mod 2 Eilenberg-MacLane spaces.

We establish that in all cases, there are only two possibilities: either the twisted homology vanishes, or it is isomorphic to untwisted homology.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Yarosh, Aliaksandraaly21@pitt.edualy21
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairSati, Hishamhsati@pitt.eduhsati
Committee MemberDeblois, Jasonjdeblois@pitt.edujdeblois
Committee MemberHales, Thomashales@pitt.eduhales
Committee MemberWesterland,
Date: 28 September 2017
Date Type: Publication
Defense Date: 2 August 2017
Approval Date: 28 September 2017
Submission Date: 9 August 2017
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 73
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: twisted cohomology, generalized cohomology, k-theory, morava k-theory
Date Deposited: 29 Sep 2017 01:17
Last Modified: 29 Sep 2017 01:17

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