Contemporary Trends in Algebraic Geometry and Algebraic Topology

10.1142/4966 ◽  
2002 ◽  
Author(s):  
Shiing-Shen Chern ◽  
Lei Fu ◽  
Richard Hain
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Topology

THE MAIN TRENDS OF ALGEBRAIC TOPOLOGY AND ALGEBRAIC GEOMETRY

1964 ◽  
Vol 19 (6) ◽  
pp. 67-73
Author(s):  
S P Novikov ◽  
I I Pyatetskii-Shapiro ◽  
I R Shafarevich
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Topology

scholarly journals THE UNITY AND IDENTITY OF DECIDABLE OBJECTS AND DOUBLE-NEGATION SHEAVES

2018 ◽  
Vol 83 (04) ◽  
pp. 1667-1679
Author(s):  
MATÍAS MENNI
Keyword(s):  
Differential Geometry ◽  
Algebraic Geometry ◽  
Algebraic Topology ◽  
Full Subcategory ◽  
Sufficient Conditions ◽  
Double Negation ◽  
Synthetic Differential Geometry ◽  
Simplicial Sets ◽  
Image Position

AbstractLet ${\cal E}$ be a topos, ${\rm{Dec}}\left( {\cal E} \right) \to {\cal E}$ be the full subcategory of decidable objects, and ${{\cal E}_{\neg \,\,\neg }} \to {\cal E}$ be the full subcategory of double-negation sheaves. We give sufficient conditions for the existence of a Unity and Identity ${\cal E} \to {\cal S}$ for the two subcategories of ${\cal E}$ above, making them Adjointly Opposite. Typical examples of such ${\cal E}$ include many ‘gros’ toposes in Algebraic Geometry, simplicial sets and other toposes of ‘combinatorial’ spaces in Algebraic Topology, and certain models of Synthetic Differential Geometry.

scholarly journals Tōhoku

2015 ◽  
Vol 1 (3) ◽  
Author(s):  
Rick Jardine
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Topology ◽  
Turning Point ◽  
Homological Algebra ◽  
Modern Mathematics

Rick Jardine evaluates Alexander Grothendieck’s 1957 mathematical masterpiece, Some Aspects of Homological Algebra, a turning point in homological algebra, algebraic topology and algebraic geometry, and for modern mathematics as a whole.

Thirteen Papers on Group Theory, Algebraic Geometry and Algebraic Topology

1968 ◽  
Author(s):  
A. Andrianov ◽  
V. Dem′janenko ◽  
S. Demuškin ◽  
N. Efimov ◽  
N. Fel′dman ◽  
...  
Keyword(s):  
Algebraic Geometry ◽  
Group Theory ◽  
Algebraic Topology

The Applications of Group Theory

2012 ◽  
Vol 430-432 ◽  
pp. 1265-1268
Author(s):  
Xiao Qiang Guo ◽  
Zheng Jun He
Keyword(s):  
Number Theory ◽  
Algebraic Geometry ◽  
Group Theory ◽  
Algebraic Number ◽  
Algebraic Topology ◽  
Polynomial Equation ◽  
Algebraic Number Theory ◽  
Simple Groups ◽  
Finite Simple Groups

Since the classification of finite simple groups completed last century, the applications of group theory are more and more widely. We first introduce the connection of groups and symmetry. And then we respectively introduce the applications of group theory in polynomial equation, algebraic topology, algebraic geometry , cryptography, algebraic number theory, physics and chemistry.

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