A Structure Theorem for RO(C2)-graded Cohomology

Let C2 be the cyclic group of order two. We present a structure theorem for the RO(C2)-graded Bredon cohomology of C2-spaces using coefficients in the constant Mackey functor F2. We show that, as a module over the cohomology of the point, the RO(C2)-graded cohomology of a finite C2-CW complex decomposes as a direct sum of two basic pieces: shifted copies of the cohomology of a point and shifted copies of the cohomologies of spheres with the antipodal action. The shifts are by elements of RO(C2) corresponding to actual (i.e. non-virtual) C2-representations.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Department of Mathematics

Grantor dc:publisher

University of Oregon

Year dc:date.issued

2018

Author dc:creator

• May, Clover

Advisor dc:contributor.advisor

• Dugger, Daniel

Statement dc:rights

• All Rights Reserved.

Language dc:language.iso

en_US

Handle dc:identifier.uri

https://hdl.handle.net/1794/23748

OAI record oai:identifier

https://scholarsbank.uoregon.edu/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Ascholarsbank.uoregon.edu%3A1794%2F23748