Digital cohomology groups of certain minimal surfaces
محورهای موضوعی : Algebraic topology
I. Karaca
1
(Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey.)
O. Ege
2
(Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey.)
کلید واژه: Digital image, universal coefficient theorem, digital cohomology group,
چکیده مقاله :
In this study, we compute simplicial cohomology groups with different coefficientsof a connected sum of certain minimal simple surfaces by using the universal coefficienttheorem for cohomology groups. The method used in this paper is a different way to computedigital cohomology groups of minimal simple surfaces. We also prove some theorems relatedto degree properties of a map on digital spheres.
[1] H. Arslan, I. Karaca, A. Oztel, Homology groups of n-dimensional digital images, XXI. Turkish National Mathematics Symposium, B (2008), 1-13.
[2] G. Bertrand, Simple points, topological numbers and geodesic neighborhoods in cubic grids, Pattern Recognit. Lett. 15 (1994), 1003-1011.
[3] G. Bertrand, R. Malgouyres, Some topological properties of discrete surfaces, J. Math. Imaging Vis. 11 (1999), 207-211.
[4] L. Boxer, A classical construction for the digital fundamental group, J. Math. Imaging Vis. 10 (1999), 51-62.
[5] L. Boxer, Digital products, wedges and covering spaces, Appl. Math. 1 (2010), 377-386.
[6] L. Boxer, Digitally continuous functions, Pattern Recognit. Lett. 15 (1994), 833-839.
[7] L. Boxer, Homotopy properties of sphere-like digital images, J. Math. Imaging Vis. 24 (2006), 167-175.
[8] L. Boxer, Properties of digital homotopy, J. Math. Imaging Vis. 22 (2005), 19-26.
[9] L. Boxer, I. Karaca, A. Oztel, Topological invariants in digital images, J. Math. Sci. Adv. Appl. 11 (2) (2011), 109-140.
[10] E. U. Demir, I. Karaca, Simplicial homology groups of certain digital surfaces, Hacet. J. Math. Stat. 44 (5) (2015), 1011-1022.
[11] O. Ege, I. Karaca, Cohomology theory for digital images, Rom. J. Inf. Sci. Tech. 16 (1) (2013), 10-28.
[12] R. Gonzalez-Diaz, A. Ion, M. I. Ham, W. G. Kropatsch, Invariant representative cocycles of cohomology generators using irregular graph pyramids, Comput. Vis. Image Underst. 115 (7) (2011), 1011-1022.
[13] R. Gonzalez-Diaz, P. Real, On the cohomology of 3D digital images, Discrete Appl. Math. 147 (2-3) (2005), 245-263.
[14] S. E. Han, An extended digital (k0,k1)-continuity, J. Appl. Math. Comput. 16 (1-2) (2004), 445-452.
[15] S. E. Han, Connected sum of digital closed surfaces, Inform. Sci. 176 (2006), 332-348.
[16] G. T. Herman, Oriented surfaces in digital spaces, CVGIP: Graphical Models and Image Processing 55 (1993), 381-396.
[17] T. Kaczynski, M. Mrozek, The cubical cohomology ring: an algorithmic approach, Found. Comput. Math. 13 (2013), 789-818.
[18] I. Karaca, G. Burak, Simplicial relative cohomology rings of digital images, Appl. Math. Inform. Sci. 8 (5) (2014), 2375-2387.
[19] A. Rosenfeld, Digital topology, Amer. Math. Monthly 86 (1979), 76-87.
[20] E. Spanier, Algebraic topology, McGraw-Hill, New York, 1966.
