Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Auckly, Dave"'
Autor:
Auckly, Dave, Giles, Betsy
This paper explores the number of parallelograms that appear in a billiard path that enters one corner of a rectangle and leaves a second corner of a rectangle as a function of the normalized dimensions of the rectangle.
Externí odkaz:
http://arxiv.org/abs/2309.01019
Autor:
Auckly, Dave
There is a relationship between the Borromean rings, the icosahedron and something called the Poincar\'e homology sphere. This relationship is explored in a wandering path that introduces fundamental ideas from topology and a geometric construction o
Externí odkaz:
http://arxiv.org/abs/2009.09836
Publikováno v:
In Topology and its Applications 15 June 2023 333
The main result of this paper is that any $3$-dimensional manifold with a finite group action is equivariantly, invertibly homology cobordant to a hyperbolic manifold; this result holds with suitable twisted coefficients as well. The following two co
Externí odkaz:
http://arxiv.org/abs/1804.03777
Any two homologous surfaces of the same genus embedded in a smooth 4-manifold X with simply-connected complements are shown to be smoothly isotopic in the connected sum of X and the product of a 2-sphere with itself, if the surfaces are ordinary, and
Externí odkaz:
http://arxiv.org/abs/1708.03208
Publikováno v:
Algebr. Geom. Topol. 17 (2017) 1771-1783
For suitable finite groups G, we construct contractible 4-manifolds C with an effective G-action on $\partial C$ whose associated pairs (C,g) for all $g \in G$ are distinct smoothings of the pair $(C,\partial C)$. Indeed C embeds in a 4-manifold so t
Externí odkaz:
http://arxiv.org/abs/1602.07650
We construct infinite families of topologically isotopic but smoothly distinct knotted spheres in many simply connected 4-manifolds that become smoothly isotopic after stabilizing by connected summing with $S^2 \times S^2$, and as a consequence, anal
Externí odkaz:
http://arxiv.org/abs/1406.4937
Autor:
Auckly, Dave
This is an expository paper designed to introduce undergraduates to the Atiyah-Singer index theorem 50 years after its announcement. It includes motivation, a statement of the theorem, an outline of the easy part of the heat equation proof. It includ
Externí odkaz:
http://arxiv.org/abs/1301.0352
Publikováno v:
In Advances in Mathematics 7 January 2019 341:609-615
Autor:
Auckly, Dave
Many three dimensional manifolds are two-fold branched covers of the three dimensional sphere. However, there are some that are not. This paper includes exposition about two-fold branched covers and many examples. It shows that there are three dimens
Externí odkaz:
http://arxiv.org/abs/1212.6282