Classification of 4 manifolds up to s-cobordism

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TVRVd01qTXo.pdf

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2015

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Beyaz, Ahmet
Pamuk, Semra
Pamuk, Mehmetcik

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Proje kapsamında gerçekleştirilen çalışmaların amacı, temel grubu belirlenmiş 4-manifoldların sınıflandırmasını manifoldlara ait temel değişmezler, temel grup, karakteristik sınıflar, kesişim formu vb, türünden yapmaktır. Öncelikli olarak temel grubunun kohomolojik boyutu 2’den küçük veya eşit olan 4-manifoldlar incelenmiştir. Bu doğrultuda Ian Hambleton ve Matthias Kreck tarafından oluşturulan örgü ve Matthias Kreck’in geliştirdiği değiştirilmiş ameliyat teorisi kullanarak, temel grubunun kohomolojik boyutu 2’den küçük veya eşit olan bazı 4-manifoldlar için skobordizm sınıflandırmasını yapmış bulunmaktayız. Bu proje kapsamında ayrıca, 4-boyutlu yönlendirilmiş Poincare eşleklik kompleksleri incelenmiştir. Poincare eşleklik kompleksleri üzerine bir sıralama bağıntısı tanımlanmış ve bu bağıntıya göre bu tür komplekslerin homotopi sınıflandırması verilmiştir. Yukarıda bahsi geçen çalışmalara ilaveten proje kapsamında hesaplamalı topoloji alanında da çalışmalara başlanmıştır.

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https://app.trdizin.gov.tr/publication/project/detail/TVRVd01qTXo
https://hdl.handle.net/11511/49766

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Department of Mathematics, Project and Design

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Citation Formats

A. Beyaz, S. Pamuk, and M. Pamuk, “Classification of 4 manifolds up to s-cobordism,” 2015. Accessed: 00, 2020. [Online]. Available: https://app.trdizin.gov.tr/publication/project/detail/TVRVd01qTXo.