A classification of semi-equivelar maps on the surface of Euler characteristic $$-1$$

2021 ◽  
Author(s):  
Debashis Bhowmik ◽  
Ashish Kumar Upadhyay
Keyword(s):  
Euler Characteristic

scholarly journals Classification of regular maps of negative prime Euler characteristic

2004 ◽  
Vol 357 (10) ◽  
pp. 4175-4190 ◽  
Author(s):  
Antonio Breda d’Azevedo ◽  
Roman Nedela ◽  
Jozef Širáň
Keyword(s):  
Euler Characteristic ◽  
Regular Maps

Periods for Continuous Self-Maps of the Figure-Eight Space

2003 ◽  
Vol 13 (07) ◽  
pp. 1743-1754 ◽  
Author(s):  
Jaume Llibre ◽  
José Paraños ◽  
J. Ángel Rodríguez
Keyword(s):  
Euler Characteristic ◽  
Connected Graph ◽  
Complete Classification ◽  
Branching Points ◽  
Branching Point

Let 8 be the graph shaped like the number 8. This paper contains a characterization of all possible sets of periods for all continuous self-maps of 8 with the branching point fixed. We remark that this characterization is the first complete classification of the sets of periods for all continuous self-maps on a connected graph with negative Euler characteristic with fixed branching points.

Structure Theory for Montgomery-Samelson Fiberings between Manifolds, II

1969 ◽  
Vol 21 ◽  
pp. 180-186 ◽  
Author(s):  
Peter L. Antonelli
Keyword(s):  
Euler Characteristic ◽  
Betti Number ◽  
Elementary Proof ◽  
Total Space ◽  
Structure Theory ◽  
Singular Set ◽  
Sphere Bundle ◽  
Simply Connected

Let f: Mn→ Npbe the projection map of an MS-fibering of manifolds β with finite non-empty singular set Aand simply connected total space (see 1). Results of Timourian (10) imply that (n, p) = (4, 3), (8, 5) or (16, 9), while a theorem of Conner (2) yields that #(A), the cardinality of the singular set, is equal to the Euler characteristic of Mn. We give an elementary proof of this fact and, in addition, prove that #(A) is actually determined by bn/2(Mn), the middle betti number of Mn, or what is the same, by bn/2(Np – f(A)). It is then shown that β is topologically the suspension of a (Hopf) sphere bundle when Np is a sphere and bn/2(Mn) = 0. It follows as a corollary that β must also be a suspension when Mn is n/4-connected with vanishing bn/2. Examples where bn/2 is not zero are constructed and we state a couple of conjectures concerning the classification of such objects.

scholarly journals Invariant Valuations on Super-Coercive Convex Functions

2019 ◽  
pp. 1-23 ◽  
Author(s):  
Fabian Mussnig
Keyword(s):  
Function Space ◽  
Euler Characteristic ◽  
Convex Functions ◽  
Legendre Transform ◽  
Translation Invariant ◽  
Characteristic Volume

Abstract All non-negative, continuous, $\text{SL}(n)$ , and translation invariant valuations on the space of super-coercive, convex functions on $\mathbb{R}^{n}$ are classified. Furthermore, using the invariance of the function space under the Legendre transform, a classification of non-negative, continuous, $\text{SL}(n)$ , and dually translation invariant valuations is obtained. In both cases, different functional analogs of the Euler characteristic, volume, and polar volume are characterized.

scholarly journals Classification of regular maps of Euler characteristic −3p

2012 ◽  
Vol 102 (4) ◽  
pp. 967-981 ◽  
Author(s):  
Marston Conder ◽  
Roman Nedela ◽  
Jozef Širáň
Keyword(s):  
Euler Characteristic ◽  
Regular Maps
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