Zobrazeno 1 - 10
of 79
pro vyhledávání: '"Gompf, Robert E."'
Autor:
Gompf, Robert E.
We show that tori in Engel 4-manifolds behave analogously to knots in contact 3-manifolds: Every torus with trivial normal bundle is isotopic to infinitely many distinct transverse tori, distinguished locally (and globally in the nullhomologous case)
Externí odkaz:
http://arxiv.org/abs/2210.04292
Autor:
Gompf, Robert E.
We study smooth, proper embeddings of noncompact surfaces in 4-manifolds, focusing on exotic planes and annuli, i.e., embeddings pairwise homeomorphic to the standard embeddings of R^2 and R^2-int D^2 in R^4. We encounter two uncountable classes of e
Externí odkaz:
http://arxiv.org/abs/2112.06051
Autor:
Gompf, Robert E.
Publikováno v:
Asian J. Math. 26 No. 5 (2022), 709-736
We study a notion of strict pseudoconvexity in the context of topologically (often unsmoothably) embedded 3-manifolds in complex surfaces. Topologically pseudoconvex (TPC) 3-manifolds behave similarly to their smooth analogues, cutting out open domai
Externí odkaz:
http://arxiv.org/abs/2010.05114
Autor:
Gompf, Robert E.
Publikováno v:
J. Differential Geom. 125 (1) (2023), 121-171
We combine Freedman's topology with Eliashberg's holomorphic theory to construct Stein neighborhood systems in complex surfaces, and use these to study various notions of convexity and concavity. Every tame, topologically embedded 2-complex K in a co
Externí odkaz:
http://arxiv.org/abs/2002.02042
Autor:
Calcut, Jack S., Gompf, Robert E.
Publikováno v:
Algebr. Geom. Topol. 19 (2019) 1299-1339
For oriented manifolds of dimension at least 4 that are simply connected at infinity, it is known that end summing is a uniquely defined operation. Calcut and Haggerty showed that more complicated fundamental group behavior at infinity can lead to no
Externí odkaz:
http://arxiv.org/abs/1801.00032
Autor:
Gompf, Robert E.
Publikováno v:
Invent. Math. 214(3) (2018), 1131--1168
We provide the first information on diffeotopy groups of exotic smoothings of R^4: For each of uncountably many smoothings, there are uncountably many isotopy classes of self-diffeomorphisms. We realize these by various explicit group actions. There
Externí odkaz:
http://arxiv.org/abs/1705.06644
Autor:
Gompf, Robert E.
Publikováno v:
Algebr. Geom. Topol. 17-5 (2017), 2863--2891
The author recently proved the existence of an infinite order cork: a compact, contractible submanifold $C$ of a 4-manifold and an infinite order diffeomorphism $f$ of $\partial C$ such that cutting out $C$ and regluing it by distinct powers of $f$ y
Externí odkaz:
http://arxiv.org/abs/1607.04354
Autor:
Gompf, Robert E.
Publikováno v:
Geom. Topol. 21 (2017) 2475-2484
We construct a compact, contractible 4-manifold $C$, an infinite-order self-diffeomorphism $f$ of its boundary, and a smooth embedding of $C$ into a closed, simply connected 4-manifold $X$, such that the manifolds obtained by cutting $C$ out of $X$ a
Externí odkaz:
http://arxiv.org/abs/1603.05090
Autor:
Gompf, Robert E.
Publikováno v:
J. Knot Theory Ramifications 26 No. 2 (2017)
This paper investigates which smooth manifolds arise as quotients (orbit spaces) of flows of vector fields. Such quotient maps were already known to be surjective on fundamental groups, but this paper shows that every epimorphism of countably present
Externí odkaz:
http://arxiv.org/abs/1501.00169
Autor:
Gompf, Robert E.
Publikováno v:
Geom. Topol. 21 (2017) 107-155
We study exotic smoothings of open 4-manifolds using the minimal genus function and its analog for end homology. While traditional techniques in open 4-manifold smoothing theory give no control of minimal genera, we make progress by using the adjunct
Externí odkaz:
http://arxiv.org/abs/1309.0466