Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
FINITE GROUP ACTIONS ON FOUR MANIFOLDS
Download
Basak_Kucuk_M_Sc__Thesis.pdf
Date
2022-7-21
Author
Küçük, Başak
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
76
views
34
downloads
Cite This
In the area of group actions on manifolds, we either fix a group G and ask the question whether G acts or not on some certain manifolds or we fix the manifold M and ask which groups can act on M in a certain way. In this thesis, we will focus on the latter; present some known and recent results about finite group actions on closed, connected, orientable four-manifolds. The group actions that are considered are topological and locally linear. We will give a detailed overview of the rank conditions of the groups G which act on both simply-connected and non-simply-connected four-manifolds by using Borel spectral sequences.
Subject Keywords
finite group actions, four-manifolds, Borel spectral sequences
URI
https://hdl.handle.net/11511/98199
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
Locally finite groups and their subgroups with small centralizers
ERSOY, KIVANÇ; Kuzucuoğlu, Mahmut; Shunwatsky, Pavel (2017-07-01)
Let p be a prime and G a locally finite group containing an elementary abelian p-subgroup A of rank at least 3 such that C-G(A) is Chernikov and C-G(a) involves no infinite simple groups for any a is an element of A(#). We show that G is almost locally soluble (Theorem 1.1). The key step in the proof is the following characterization of PSLp(k): An infinite simple locally finite group G admits an elementary abelian p-group of automorphisms A such that C-G(A) is Chernikov and C-G(A) Keywords: involves no inf...
Fixed point free action on groups of odd order
Ercan, Gülin; Güloğlu, İsmail Ş. (Elsevier BV, 2008-7)
Let A be a finite abelian group that acts fixed point freely on a finite (solvable) group G. Assume that |G| is odd and A is of squarefree exponent coprime to 6. We show that the Fitting length of G is bounded by the length of the longest chain of subgroups of A.
RELATIVE GROUP COHOMOLOGY AND THE ORBIT CATEGORY
Pamuk, Semra (2014-07-03)
Let G be a finite group and F be a family of subgroups of G closed under conjugation and taking subgroups. We consider the question whether there exists a periodic relative F-projective resolution for Z when F is the family of all subgroups HG with rkHrkG-1. We answer this question negatively by calculating the relative group cohomology FH*(G, ?(2)) where G = Z/2xZ/2 and F is the family of cyclic subgroups of G. To do this calculation we first observe that the relative group cohomology FH*(G, M) can be calc...
Equivariant cross sections of complex Stiefel manifolds
Onder, T (Elsevier BV, 2001-01-16)
Let G be a finite group and let M be a unitary representation space of G. A solution to the existence problem of G-equivariant cross sections of the complex Stiefel manifold W-k(M) of unitary k-frames over the unit sphere S(M) is given under mild restrictions on G and on fixed point sets. In the case G is an even ordered group, some sufficient conditions for the existence of G-equivariant real frame fields on spheres with complementary G-equivariant complex structures are also obtained, improving earlier re...
Finite action Yang-Mills solutions on the group manifold
Dereli, T; Schray, J; Tucker, RW (IOP Publishing, 1996-08-21)
We demonstrate that the left (and right) invariant Maurer-Cartan forms for any semi-simple Lie group enable solutions of the Yang-Mills equations to be constructed on the group manifold equipped with the natural Cartan-Killing metric. For the unitary unimodular groups the Yang-Mills action integral is finite for such solutions. This is explicitly exhibited for the case of SU(3).
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
B. Küçük, “FINITE GROUP ACTIONS ON FOUR MANIFOLDS,” M.S. - Master of Science, Middle East Technical University, 2022.