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Journal of Astrophysics & Aerospace Technology | ISSN: 2329-6542 | Volume 6
Planetary Science and Particle Physics
International Conference on
August 27-28, 2018 | Boston, USA
Topology of 4-dimensional universe for every 3-dimensional manifold
Akio Kawauchi
Osaka City University Advanced Mathematical Institute, Japan
A
4-dimensional universe is a4-dimensional boundary-less connectedorientedmanifoldwithevery3-dimensional closedconnected
oriented manifold embedded. A 4-dimensional punctured universe is a 4-dimensional boundary-less connected oriented
manifold with the punctured manifold of every 3-dimensional closed connected oriented manifold embedded. It is known that every
4-dimensional universe and every 4-dimensional punctured universe are 4-dimensional open manifolds. If a 3-dimensional closed
connected orientable manifold is considered as a 3-dimensional universe, then every spacetime is embedded in every 4-dimensional
universe since the trivial line bundle over every 3-dimensional universe is embedded in it. For any 4-dimensional oriented manifold
Y, some topological invariants of Y with values taken in {0, 1, 2, …, +∞} are defined by using homological arguments and called
the topological indexes of Y. The topological indexes are applied to a 4-dimensional punctured universe and refined notions of a
4-dimensional universe, namely 4-dimensional types 1, 2 and full universes to show certain infinity of these topological indexes.
It is shown that this infinity comes from embeddings of the connected sums of 3-dimensional homology handles obtained from
certain infinite family of knots by 0-surgery. Recently, it is also shown that the rational second homologies of every 4-dimensional
universe and every 4-dimensional punctured universe are always infinitely generated over the rationals by using the embeddings of
3-dimensional closed connected oriented manifolds obtained from the 3-torus and certain infinite family of knots. In conclusion, it is
confirmed that the topology of every 4-dimensional universe and every 4-dimensional punctured universe are related to knot theory.
kawauchi@sci.osaka-cu.ac.jpJ Astrophys Aerospace Technol 2018, Volume 6
DOI: 10.4172/2329-6542-C2-021