Space of Smooth 1-Knots in a 4-Manifold: Is Its Algebraic Topology Sensitive to Smooth Structures?

Oleg Viro

doi:10.1007/s40598-015-0007-5

Space of Smooth 1-Knots in a 4-Manifold: Is Its Algebraic Topology Sensitive to Smooth Structures?

Oleg Viro

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We discuss a possibility to get an invariant of a smooth structure on a closed simply connected 4-manifold from homotopy invariants of the space of loops smoothly embedded into the manifold.

Original language	English
Pages (from-to)	83-89
Number of pages	7
Journal	Arnold Mathematical Journal
Volume	1
Issue number	1
DOIs	https://doi.org/10.1007/s40598-015-0007-5
State	Published - Mar 1 2015

Keywords

4-manifolds
Alexander polynomial
Exotic smooth structures
Seiberg–Witten invariants
Vassiliev invariants

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10.1007/s40598-015-0007-5

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@article{09aac979875c4010adf6f6488c175ac2,

title = "Space of Smooth 1-Knots in a 4-Manifold: Is Its Algebraic Topology Sensitive to Smooth Structures?",

abstract = "We discuss a possibility to get an invariant of a smooth structure on a closed simply connected 4-manifold from homotopy invariants of the space of loops smoothly embedded into the manifold.",

keywords = "4-manifolds, Alexander polynomial, Exotic smooth structures, Seiberg{\textendash}Witten invariants, Vassiliev invariants",

author = "Oleg Viro",

note = "Publisher Copyright: {\textcopyright} 2015, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.",

year = "2015",

month = mar,

day = "1",

doi = "10.1007/s40598-015-0007-5",

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journal = "Arnold Mathematical Journal",

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T2 - Is Its Algebraic Topology Sensitive to Smooth Structures?

AU - Viro, Oleg

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Y1 - 2015/3/1

N2 - We discuss a possibility to get an invariant of a smooth structure on a closed simply connected 4-manifold from homotopy invariants of the space of loops smoothly embedded into the manifold.

AB - We discuss a possibility to get an invariant of a smooth structure on a closed simply connected 4-manifold from homotopy invariants of the space of loops smoothly embedded into the manifold.

KW - 4-manifolds

KW - Alexander polynomial

KW - Exotic smooth structures

KW - Seiberg–Witten invariants

KW - Vassiliev invariants

UR - https://www.scopus.com/pages/publications/85034664133

U2 - 10.1007/s40598-015-0007-5

DO - 10.1007/s40598-015-0007-5

M3 - Article

AN - SCOPUS:85034664133

SN - 2199-6792

VL - 1

SP - 83

EP - 89

JO - Arnold Mathematical Journal

JF - Arnold Mathematical Journal

IS - 1

ER -

Space of Smooth 1-Knots in a 4-Manifold: Is Its Algebraic Topology Sensitive to Smooth Structures?

Abstract

Keywords

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